You can
put this solution on YOUR website!# 1
Start with the given expression
Factor out the GCF
Now let's focus on the inner expression
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Looking at
we can see that the first term is
and the last term is
where the coefficients are 9 and 16 respectively.
Now multiply the first coefficient 9 and the last coefficient 16 to get 144. Now what two numbers multiply to 144 and add to the middle coefficient 24? Let's list all of the factors of 144:
Factors of 144:
1,2,3,4,6,8,9,12,16,18,24,36,48,72
-1,-2,-3,-4,-6,-8,-9,-12,-16,-18,-24,-36,-48,-72 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 144
1*144
2*72
3*48
4*36
6*24
8*18
9*16
12*12
(-1)*(-144)
(-2)*(-72)
(-3)*(-48)
(-4)*(-36)
(-6)*(-24)
(-8)*(-18)
(-9)*(-16)
(-12)*(-12)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 24? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 24
| First Number | Second Number | Sum | | 1 | 144 | 1+144=145 |
| 2 | 72 | 2+72=74 |
| 3 | 48 | 3+48=51 |
| 4 | 36 | 4+36=40 |
| 6 | 24 | 6+24=30 |
| 8 | 18 | 8+18=26 |
| 9 | 16 | 9+16=25 |
| 12 | 12 | 12+12=24 |
| -1 | -144 | -1+(-144)=-145 |
| -2 | -72 | -2+(-72)=-74 |
| -3 | -48 | -3+(-48)=-51 |
| -4 | -36 | -4+(-36)=-40 |
| -6 | -24 | -6+(-24)=-30 |
| -8 | -18 | -8+(-18)=-26 |
| -9 | -16 | -9+(-16)=-25 |
| -12 | -12 | -12+(-12)=-24 |
From this list we can see that 12 and 12 add up to 24 and multiply to 144
Now looking at the expression
, replace
with
(notice
adds up to
. So it is equivalent to
)
Now let's factor
by grouping:
Group like terms
Factor out the GCF of
out of the first group. Factor out the GCF of
out of the second group
Since we have a common term of
, we can combine like terms
So
factors to
So this also means that
factors to
(since
is equivalent to
)
note:
is equivalent to
since the term
occurs twice. So
also factors to
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So our expression goes from
and factors further to
------------------
Answer:
So
factors to
In other words
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# 2
Start with the given expression.
Rewrite
as
. Rewrite
as
.
Now factor by using the sum of cubes formula. Remember the
sum of cubes formula is
Multiply
-----------------------------------
Answer:
So
factors to
.
In other words,
(