You can put this solution on YOUR website!
I'm not sure what you mean by the box method, but here's one way to do it.
Looking at the expression
, we can see that the first coefficient is
, the second coefficient is
, and the last term is
Now multiply the first coefficient
by the last term
Now the question is: what two whole numbers multiply to
(the previous product) and
add to the second coefficient
To find these two numbers, we need to list all
of the factors of
(the previous product).
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to
1*80 = 80
2*40 = 80
4*20 = 80
5*16 = 80
8*10 = 80
(-1)*(-80) = 80
(-2)*(-40) = 80
(-4)*(-20) = 80
(-5)*(-16) = 80
(-8)*(-10) = 80
Now let's add up each pair of factors to see if one pair adds to the middle coefficient
|First Number||Second Number||Sum|
From the table, we can see that the two numbers
(the middle coefficient).
So the two numbers
both multiply to and
Now replace the middle term
. So this shows us that
Replace the second term
Group the terms into two pairs.
Factor out the GCF
from the first group.
from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.
Combine like terms. Or factor out the common term
In other words,
Note: you can check the answer by expanding
or by graphing the original expression and the answer (the two graphs should be identical).