College Algebra & Trigonometry, 2018a

24 CHAPTER 1. ALGEBRA REVIEW
Difference of Squares
Factoring a difference of squares is actually a special form of trinomial factoring.
If we consider a trinomial of the form ax 2 + bx + c, where c is a perfect square and
negative, we will find something interesting about the possible values of b that
make the trinomial factorable.
Example
Consider x 2 + bx − 36
For this expression to be factorable, the middle coefficient b would need to be
equal to the difference of any of the factor pairs of 36. If we look at the possible
factor pairs, we see the following:
1 36
2 18
3 12
4 9
6 6
This means that the possible values for b that would make this expression factorable
are:
36 − 1=35→ x 2 +35x − 36 = (x + 36)(x − 1)
18 − 2=16→ x 2 +16x − 36 = (x + 18)(x − 2)
12 − 3=9→ x 2 +9x − 36 = (x + 12)(x − 3)
9 − 4=5→ x 2 +5x − 36 = (x +9)(x − 4)
6 − 6=0→ x 2 +0x − 36 = x 2 − 36 = (x +6)(x − 6)