You can
put this solution on YOUR website!Are you sure it's not supposed to read:
???
Start with the given expression
Combine like terms
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 1 and -6 respectively.
Now multiply the first coefficient 1 and the last coefficient -6 to get -6. Now what two numbers multiply to -6 and add to the middle coefficient 1? Let's list all of the factors of -6:
Factors of -6:
1,2,3,6
-1,-2,-3,-6 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -6
(1)*(-6)
(2)*(-3)
(-1)*(6)
(-2)*(3)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1
| First Number | Second Number | Sum | | 1 | -6 | 1+(-6)=-5 |
| 2 | -3 | 2+(-3)=-1 |
| -1 | 6 | -1+6=5 |
| -2 | 3 | -2+3=1 |
From this list we can see that -2 and 3 add up to 1 and multiply to -6
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
)
------------------------------------------------------------
So our expression goes from
and factors further to
------------------
Answer:
So
factors to
(