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ACT Aspire Math: Recognizing Equivalent Expressions 1 Views


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Description:

If a + b = 1, what is another way to write a(1 – a)?


Transcript

00:03

Okay A c t math aspiring shmoop er's and everyone

00:07

Here we go If a plus b is one what's

00:09

another way to write a times quantity one minus a

00:16

The problem wants us to rewrite a times quantity one

00:19

minus a And judging from the answer choices it wants

00:22

us to introduce some bee in there The easiest way

00:25

to do this problem is to stage a mini rebellion

00:27

against outrun all its variables Since the answer choices are

00:30

all in variables and we're not told what a times

00:33

twenty one months actually is equal to Well then we

00:36

can make up our own numbers That's fun Dish Let

00:39

equals three Let's be equal Negative too And this works

00:42

because while a plus b is three plus negative to

00:47

which equals one so phase three then we can solve

00:50

a times quantity one one say is eight times one

00:53

is three times one ministry which is three times thing

00:57

too So eight times condominium is negative Six All right

01:01

well a bung The answer Choices We're looking for another

01:03

expression that equals negative six when a is three and

01:07

b is negative too Well the only one that fits

01:09

the bill is a b That's the answer D there

01:12

since three times Negative too is negative Six What's that

01:16

you say Your algebra teacher is standing right behind you

01:19

With a ruler All right we get it The timing

01:21

just isn't right for your rebellion Put your weaponized imagers

01:24

down and solve this problem Algebraic lee realigning or rearranging

01:29

the first equation so that we can see a in

01:31

terms of b So it looks like this a plus

01:33

b is one and then a equals one minus b

01:35

But does the problem want us to completely get rid

01:37

of a or should we mix it up a bit

01:39

It's unclear from the answer choices so we substitute in

01:42

one minus b for only the second day and it

01:45

allows us to mix it up in just the right

01:47

way to get the answers That looks like this where

01:49

eight times quantity one might say is eight times the

01:52

quantity one minus quantity one minus b which is the

01:55

same Asked a times twenty zero plus b which is

01:58

the same as well just eight times b Well finding

02:01

just the right mix may have taken you sometime and

02:03

since you also could have tried substituting the first term

02:06

a There are on ly on That's what it would

02:08

have looked like or you could have tried getting rid

02:11

of it altogether translating the entire expression into b That's

02:14

what it would have looked like But the answer is 00:02:17.465 --> [endTime] d eight times being all right we're done

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