Section 6-6

Multiplying Polynomials: Special Cases (Perfect Squares, Product of a Sum and a Difference)

There are two special cases when multiplying polynomials, which have easy patterns you should memorize. These are the square of a binomial pattern and the product of a sum and a difference pattern.

SQUARE OF A BINOMIAL

This is the special case in which you are asked to multiply

(x + a)(x + a).

Using FOIL, we get:

= x² + ax + ax + a²

= x² + 2ax + a²

Using the binomial square pattern with a = –6, we get:

(p – 6)(p – 6) = p² + 2(–6p) + (–6)²

= p² – 12p + 36

PRODUCT OF A SUM AND A DIFFERENCE

The product of a sum and a difference of the same two expressions can be written as a difference of squares.

(x + a)(x – a)

Using FOIL, we get

x² – ax + ax – a²

= x²– a²

Using the product of a sum and a difference pattern, we get:

(r³ + s)(r³– s)

= r⁶– s²