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Example 2: Finding the square of a binomial with one variable | Algebra I | Khan Academy

Video vocabulary

here

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US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

already

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US / ɔ:lˈredi /

UK / ɔlˈrɛdi /

A1
  • adverb
  • Having happened or been done before this time

realize

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US / 'ri:əlaɪz /

UK / ˈriəˌlaɪz /

A1
  • verb
  • To become aware of or understand mentally

guess

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US / ɡes /

UK / ɡɛs /

A1
  • noun
  • Answer given when you don't know if it is correct
  • verb
  • To give an answer without knowing if it is correct

temptation

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US / tempˈteɪʃn /

UK / tɛmpˈteʃən /

A2
  • noun
  • Something making you want to do/have bad thing

straight

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US / streɪt /

UK / stret /

A2
  • adjecitve
  • Not having curves, bends, or angles
  • Not gay; heterosexual
  • honest and direct
  • adverb
  • in a line; immediately; honestly and directly

use

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US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

will

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US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

itself

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US / ɪtˈself /

UK / ɪtˈsɛlf /

A1
  • pronoun
  • Referring to it

should

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US / ʃʊd /

UK / ʃʊd /

A1
  • other
  • Used to indicate what is proper or reasonable

plus

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US / plʌs /

UK / plʌs /

A2
  • noun
  • A benefit or advantage
  • preposition
  • In addition; add
  • In addition to; Indicates a number above
  • Having a value greater than zero

actually

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US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

write

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US / raɪt /

UK / raɪt /

A1
  • verb
  • To compose letters and words on paper or a screen
  • To invent or create a computer program
  • To create a song or piece of music

exactly

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US / ɪgˈzæktli /

UK / ɪɡˈzæktli /

A1
  • adverb
  • No more and no less than; precisely

once

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US / wʌns /

UK / wʌns /

A1
  • adverb
  • One time; one instance
  • At a time in the past
  • conjunction
  • When; as soon as

see

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US / si: /

UK / si /

A1
  • verb
  • To go on a date with someone
  • To predict whether something is, or will be true
  • To understand what someone says
  • To use your eyes to look at something
  • To visit a place often for sightseeing or pleasure
  • To visit or meet with someone
  • To find out by waiting or looking
  • To watch (a game, movie or TV show)

part

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US / pɑ:t /

UK / pɑ:rt /

A1
  • adjecitve
  • To some degree; half; not fully
  • noun
  • Division of a book
  • Ratio of something, e.g. 3 of gin, 1 of tonic
  • A line in a person's hair, made with a comb
  • Character an actor plays on stage, movie, or TV
  • Some, but not all of a specific thing
  • Role in causing something to happen
  • verb
  • To make a line in a person's hair, by using a comb
  • To move two things apart creating a space
  • To leave someone, or to break off a relationship

problem

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US / ˈprɒbləm /

UK / ˈprɑbləm /

A1
  • adjecitve
  • Causing trouble
  • noun
  • Something difficult to deal with or causes trouble
  • Question to show understanding of a math concept

have

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US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

could

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US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

over

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US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

completely

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US / kəmˈpli:tli /

UK / kəmˈpliːtli /

A1
  • adverb
  • In every way or as much as possible

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

another

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US / əˈnʌðə(r) /

UK / əˈnʌðɚ /

A1
  • adjecitve
  • One more, but not this
  • determiner
  • One more added
  • pronoun
  • One more (thing)

only

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US / ˈəunli /

UK / ˈonli /

A1
  • adverb
  • Just one; just that amount or thing; not more than
  • Not very important or serious
  • Just that type of thing, person
  • Short time ago; not before a certain time
  • conjunction
  • Except; but

any

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US / 'enɪ /

UK / ˈɛni /

A1
  • adjecitve
  • One, or some, no matter which
  • pronoun
  • One (thing) of many; some

lot

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US / lɒt /

UK / lɑt /

A1
  • noun
  • What happens to a person in life from chance; fate
  • A group of people seen together
  • Item for sale at an auction
  • Small area of land used for a purpose e.g. parking

out

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US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

something

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US / ˈsʌmθɪŋ /

UK / ˈsʌmθɪŋ /

A1
  • adverb
  • In some degree or measure
  • noun
  • a person or thing of some value or consequence
  • pronoun
  • Thing that is not yet known or named
  • Approximately

think

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US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

come

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US / kʌm /

UK / kʌm /

A1
  • verb
  • To arrive at a place
  • (Of mail) to be delivered
  • To move toward someone; go with someone
  • To reach a certain point or state

general

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US / 'dʒenrəl /

UK / ˈdʒɛnərəl /

A1
  • adjecitve
  • Widespread, normal or usual
  • noun
  • Top ranked officer in the army

way

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US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

all

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US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

between

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US / bɪˈtwi:n /

UK / bɪˈtwin /

A1
  • preposition
  • From one person, thing, or place, to another
  • In the space that separates two objects
  • Among two or more people who share something

cap

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US / kæp /

UK / kæp /

B1
  • noun
  • Covering for the end or top of something
  • Small, soft hat often with a front visor or shade
  • An upper limit on the amount of (e.g. budget)
  • verb
  • To cover the top or end of an object
  • To limit the amount of usage of something

multiply

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US / ˈmʌltɪplaɪ /

UK / ˈmʌltəˌplaɪ /

B1
  • verb
  • To increase in number by reproducing/having babies
  • To increase something by a large quantity
  • To have increased by a large quantity
  • To calculate two numbers e.g. 2 x 4

huge

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US / hju:dʒ /

UK / hjudʒ /

A2
  • adjecitve
  • Very very large

look

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US / lʊk /

UK / lʊk /

A1
  • noun
  • Person's beauty or physical attractiveness
  • Particular style of dress, clothes, or appearance
  • The way someone, something appears to be
  • Act of searching for or examining something
  • verb
  • To appear to be; seem

add

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US / æd /

UK / æd /

A1
  • verb
  • To include as well
  • To put two things or numbers together, e.g. 2+2

swap

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US / swɒp /

UK / swɑp /

B2
  • noun
  • A trade or exchange of goods without using money
  • verb
  • To exchange goods without spending money; trade

show

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US / ʃəʊ /

UK / ʃo /

A1
  • noun
  • False display of love, emotion or action
  • An event for displaying or promoting goods
  • Play, opera or theater production
  • Presentation that is broadcast on TV or radio
  • verb
  • To be easily seen or displayed
  • To display your emotions or feelings
  • To let someone see something; display
  • To explain or teach how something is done
  • To lead someone somewhere; point them to something
  • To prove something to be true, correct
  • To reveal or allow something to be seen

they

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US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

pattern

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US / 'pætn /

UK / ˈpætən /

A2
  • noun
  • Model to follow in making or doing something
  • Colors or shapes which are repeated on objects
  • Regular repeated behavior
  • verb
  • To copy the way something else is made

distribute

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US / dɪˈstrɪbju:t /

UK / dɪˈstrɪbjut /

A2
  • verb
  • To hand out or give to people
  • To send products to stores to sell
  • To spread something over an area

would

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US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

now

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US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

really

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US / ˈri:əli /

UK / ˈriəˌli, ˈrili /

A1
  • adverb
  • Used to stress something that is said; definitely
  • In a true or accurate manner
  • Very

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

apply

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US / ə'plaɪ /

UK / əˈplaɪ /

A1
  • verb
  • To spread a substance or liquid over a surface
  • To commit your time and effort to doing something
  • To make something useful in a certain situation
  • To be relevant for a situation
  • To ask formally for (job, permission etc.)

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

can

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US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

not

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US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

give

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US / ɡɪv /

UK / ɡɪv /

A1
  • noun
  • Degree of flexibility in something, a material
  • verb
  • To hand over or present something to someone
  • To cause someone to have or experience something

equal

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US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

same

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US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

want

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US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

answer

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US / 'ɑ:nsə(r) /

UK / ˈænsɚ /

A1
  • noun
  • Reply to a question someone asks
  • Solution to a problem or test question
  • verb
  • To reply to a question someone asks
  • To solve a test question or a problem

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

one

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US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

highlight

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US / ˈhaɪlaɪt /

UK / ˈhaɪˌlaɪt /

A2
  • noun
  • Best or most interesting part of something
  • Spot or section lighter than the area around it
  • verb
  • To use chemicals to make some hair a lighter color
  • To make people aware of a problem, subject, issue
  • To focus particular attention on; draw attention
  • To use a pen to mark places of interest in a book

term

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US / tɜ:m /

UK / tɚm /

A1
  • noun
  • Conditions applying to an agreement, contract
  • Length of time something is expected to happen
  • Fixed period of weeks for learning at school
  • The (precise) name given to something
  • verb
  • To call; give a name to

might

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US / maɪt /

UK / maɪt /

A1
  • other
  • Used to politely request an action
  • Used to express that something could happen
  • Power, strength, force or influence

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

foil

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US / fɔɪl /

UK / fɔɪl /

B2
  • noun
  • Very thin layer of metal
  • verb
  • To cleverly prevent (plot/crime) from happening

this

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US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

power

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US / 'paʊə(r) /

UK / ˈpaʊɚ /

A1
  • noun
  • Legal or official right to perform certain actions
  • Ability to move forcefully and quickly
  • Energy of something (e.g. electricity or fuel)
  • Mathematical way to multiply a number
  • Condition of being in political control
  • Physical force, energy, and strength
  • verb
  • To give energy to something, e.g. by electricity
  • To move something forcefully and quickly

the

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US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

order

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US / 'ɔ:də(r) /

UK / ˈɔrdɚ /

A1
  • noun
  • Religious or social group, as of nuns
  • Instructions to others to do what you want
  • State in which things are neat and organized
  • What you ask to buy, e.g. food in restaurant
  • Social or political control of an area
  • verb
  • To put things in a sequence, e.g. a, b, c
  • To give instructions to others to do what you want
  • To ask for something you want to buy, e.g. a meal

other

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US / 'ʌðə(r) /

UK / ˈʌðər /

A1
  • adjecitve
  • A thing different from that mentioned
  • determiner
  • (Something) else; not the first (one)
  • pronoun
  • Being the one and only thing of that category

square

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US / skweə(r) /

UK / skwɛr /

A2
  • adjecitve
  • Being fair or honest
  • Multiply a number by itself e.g. 2x2 or 6x6
  • noun
  • Shape with 4 equal length sides and 4 equal angles
  • The result of multiplying Length by the width
  • Open public area in the middle of the town
  • verb
  • To make something balance or be equal
  • To multiply a number by itself, e.g. 2x2 or 6x8
  • To straighten the edge to form a four-sided shape

happen

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US / 'hæpən /

UK / ˈhæpən /

A1
  • verb
  • To take place or occur

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

get

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US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

what

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US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

mean

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US / mi:n /

UK / min /

A1
  • adjecitve
  • Being good at
  • Nasty; unkind
  • Not liking to spend money; cheap; stingy
  • noun
  • Average of a set of numbers
  • verb
  • To express a particular idea or thought
  • To intend to do something in particular
  • To have a particular meaning or value

about

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US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

different

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US / ˈdɪfrənt /

UK / ˈdɪfrənt /

A1
  • adjecitve
  • Not of the same kind; unlike other things

each

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US / i:tʃ /

UK / itʃ /

A1
  • determiner
  • Every one of two or more things
  • pronoun
  • Per one person or thing

like

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US / laɪk /

UK / laɪk /

A1
  • adjecitve
  • Being equal in status or kind to something else
  • Similar; the same
  • adverb
  • For example
  • preposition
  • Used as a filler; used to ad emphasis
  • In a way similar to the way something is done
  • Such as; for example
  • verb
  • To want to
  • To find something pleasing; to prefer something

method

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US / 'meθəd /

UK / ˈmɛθəd /

A2
  • noun
  • (Organized and planned) way of doing something

twice

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US / twaɪs /

UK / twaɪs /

A1
  • adverb
  • Two times

case

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US / keɪs /

UK / kes /

A1
  • noun
  • Container used to carry things, e.g. clothes
  • Set of facts about a crime
  • Set of facts about an event
  • Example or instance of something
  • verb
  • To find out about a place, as in planning to steal

first

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US / fɜ:st /

UK / fɚst /

A1
  • adjecitve
  • 1st; Coming before all others in time or place
  • noun
  • Something that has not happened before
  • Position of the winner of a competition

expand

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US / ɪk'spænd /

UK / ɪkˈspænd /

A2
  • verb
  • To make something larger in size, number, amount

number

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US / ˈnʌmbə(r) /

UK / ˈnʌmbɚ /

A1
  • noun
  • Symbols such as 1, 2, 56, 793
  • Particular song or dance performed during a show
  • Total quantity or amount of things
  • verb
  • To put numbers on things
  • To assign a sequence within a group, series, set
  • To claim to be part of a larger group, series, set

remind

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US / rɪ'maɪnd /

UK / rɪˈmaɪnd /

A2
  • verb
  • To cause someone to remember what they forgot

then

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US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

second

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US / 'sekənd /

UK / ˈsɛkənd /

A1
  • adjecitve
  • 2nd; the one following first
  • noun
  • Unit of time; one sixtieth of a minute
  • Short period of time that you wait for someone
  • (Do) soon

right

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US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

people

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US / 'pi:pl /

UK / ˈpipəl /

A1
  • noun
  • Persons sharing culture, country, background, etc.
  • Men, Women, Children

ask

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US / ɑ:sk /

UK / æsk /

A1
  • verb
  • To say to someone that you want something

time

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US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

difference

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US / 'dɪfrəns /

UK / ˈdɪfərəns, ˈdɪfrəns /

A1
  • noun
  • A thing or issue that people do not agree about
  • Not of the same kind; unlike other things

exact

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US / ɪɡ'zækt /

UK / ɪɡˈzækt /

A2
  • adjecitve
  • Completely correct; accurate; specific
  • verb
  • To get something, sometimes using force

distributive

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US / dɪˈstrɪbjətɪv /

UK / dɪˈstrɪbjətɪv /

B1
  • adjecitve
  • Serving to distribute or allot or disperse

special

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US / 'speʃl /

UK / ˈspɛʃəl /

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  • adjecitve
  • Being additional or extra
  • Different, better or greater than normal
  • noun
  • Heavily discounted sales item

middle

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US / 'mɪdl /

UK / ˈmidl /

A1
  • adjecitve
  • Equal distance from extremes
  • noun
  • Place that is halfway between two things

why

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US / waɪ /

UK / hwaɪ, waɪ /

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  • adverb
  • Question word to ask for a reason
  • exclamation
  • (Used to express surprise or approval)

combination

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US / ˌkɒmbɪ'neɪʃn /

UK / ˌkɑmbəˈneʃən /

B1
  • noun
  • Series of letters or numbers needed to open a lock
  • Act or result of mixing things together

yourself

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US / jɔ:ˈself /

UK / jʊrˈsɛlf, jɔr-, jor-, jə- /

A1
  • pronoun
  • Reflexive form of 'you', used for an emphasis

just

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US / dʒʌst /

UK / dʒʌst /

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  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)
  • Subtitles section
  • We're asked to simplify or to expand 7x plus 10 to the second power.
  • Now, the first thing I will show you is exactly what you should not do.
  • There's a huge temptation.
  • A lot of people will look and they'll say, oh, that's 7x squared plus 10 squared.
  • This is wrong.
  • And I'll write it in caps.
  • This is wrong.
  • What your brain is doing is thinking, oh, if I had 7x times 10 and I squared that, this would be 7x squared times 10 squared.
  • We aren't multiplying here.
  • We're adding 7x to 10. So you can't just square each of these terms.
  • I just wanted to highlight, this is completely wrong.
  • And to see why it's wrong, you have to just remind yourself that 7x plus 10 squared, this is the exact same thing as 7x plus 10 times 7x plus 10. That's what it means to square something.
  • You're multiplying it by itself, I guess, twice here.
  • If you only did it once, you'd only have one 7x plus 10. So this is what it is.
  • So we're really just multiplying a binomial or two binomials.
  • They just happen to be the same one.
  • And you could use FOIL.
  • You could use the distributive method.
  • But this is actually a special case.
  • When you're squaring a binomial.
  • So let's just think about it as a special case first.
  • And we can apply whatever we learn to this.
  • So we could have just done it straight here.
  • But I want to learn the general case.
  • So you can apply it to any problem that you might see.
  • So if I have a plus b squared, we already realize that's not a squared plus b squared.
  • That is a plus b times a plus b.
  • And now we can use the distributive property.
  • We can distribute this a plus b times this a.
  • So we get a times a plus b.
  • And then we could distribute the a plus b times this b.
  • Plus b times a plus b.
  • And then we distribute this a.
  • We get a squared plus ab.
  • Plus b times a is another ab.
  • And I'm just swapping the order so it's the same as this.
  • Plus b times b, which is b squared.
  • These are the same.
  • Or these are like terms.
  • So we can add them.
  • One of something plus another of that something will give you two of that something.
  • 2ab.
  • We have a squared plus 2ab plus b squared.
  • So the pattern here, if I have a plus b squared, it's equal to a squared plus 2 times the product of these numbers plus b squared.
  • So over here I have 7x plus 10 squared.
  • So this is going to be equal to 7x squared plus 2 times the product of 7x and 10. 2 times 7x times 10. Plus 10 squared.
  • So the difference between the right answer and the wrong answer is that you have this middle term here that you might have forgotten about if you did it this way.
  • And this comes out when you're multiplying all of the different combinations of the terms here.
  • And if we simplify this, if we simplify it, 7x squared, that's 7 squared times x squared.
  • So 7 squared is 49 times x squared.
  • When you multiply this part out, 2 times 7 times 10, that's 14 times 10, which is 140.
  • And then we have our x.
  • No other x there.
  • And then plus 10 squared.
  • So plus 100.
  • And we are done.