Special Cases of Binomial Multiplication Examples Page 2

Find two binomials that multiply together to give 25x² - 9.

This is a difference of two squares, so it looks like the answer to a multiplication of the form

(▲ + ■)(▲ - ■).

We need to figure out what ▲ and ■ are. We will need to work backwards for this one. Use your rear view mirror and proceed cautiously.

Since

(▲)²=25x²,

we have

▲ = ± 5x.

Similarly, since

(■)² = 9,

we must have

■ = ± 3.

Two binomials that multiply together to give 25x² - 9 are

(5x + 3) and (5x - 3).

To check our answer, we can perform the multiplication (5x + 3)(5x - 3).

We could have used -5x instead of 5x and/or -3 instead of 3. Either way will work, but for this sort of problem we pick the positive square roots because we're trying to make things look tidy and unnecessary negative signs are messy. Like they say, a messy expression is a sign of a disorganized mind.