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Start with the given expression
Factor out the GCF
Now let's focus on the inner expression
Looking at
we can see that the first term is
and the last term is
where the coefficients are 5 and -3 respectively.
Now multiply the first coefficient 5 and the last coefficient -3 to get -15. Now what two numbers multiply to -15 and add to the middle coefficient 14? Let's list all of the factors of -15:
Factors of -15:
1,3,5,15
-1,-3,-5,-15 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -15
(1)*(-15)
(3)*(-5)
(-1)*(15)
(-3)*(5)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to 14? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 14
| First Number | Second Number | Sum | | 1 | -15 | 1+(-15)=-14 |
| 3 | -5 | 3+(-5)=-2 |
| -1 | 15 | -1+15=14 |
| -3 | 5 | -3+5=2 |
From this list we can see that -1 and 15 add up to 14 and multiply to -15
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
)
Now reintroduce the GCF
-------------------------------
Answer:
So
factors to
(