# ACT Aspire Math: Recognizing Equivalent Expressions

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

ACT Aspire | Math |

ACT Aspire Math | Algebra |

Math | Algebra |

Product Type | ACT Aspire |

Test Prep | ACT Aspire ACT Aspire Math |

### Transcript

us to introduce some bee in there The easiest way

to do this problem is to stage a mini rebellion

against outrun all its variables Since the answer choices are

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

twenty one months actually is equal to Well then we

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

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

because while a plus b is three plus negative to

which equals one so phase three then we can solve

a times quantity one one say is eight times one

is three times one ministry which is three times thing

too So eight times condominium is negative Six All right

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

expression that equals negative six when a is three and

b is negative too Well the only one that fits

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

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

you say Your algebra teacher is standing right behind you

With a ruler All right we get it The timing

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

down and solve this problem Algebraic lee realigning or rearranging

the first equation so that we can see a in

terms of b So it looks like this a plus

b is one and then a equals one minus b

But does the problem want us to completely get rid

of a or should we mix it up a bit

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

one minus b for only the second day and it

allows us to mix it up in just the right

way to get the answers That looks like this where

eight times quantity one might say is eight times the

quantity one minus quantity one minus b which is the

same Asked a times twenty zero plus b which is

the same as well just eight times b Well finding

just the right mix may have taken you sometime and

since you also could have tried substituting the first term

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

have looked like or you could have tried getting rid

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

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