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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
Full Transcript
- 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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