Factoring the Difference of Two Squares

The difference of two terms with “square coefficients”and “even exponents” will always be factored as the difference of squares.

49x⁴ − 36y⁴

(7x² + 6y²)(7x² − 6y²)

Sometimes the factors themselves contain a factorable binomial

→ difference of squares.

Another difference of squares. Continue factoring:

Continue factoring to prime factors:

x⁸ − y⁸ = (x⁴ + y⁴)(x⁴ − y⁴)

= (x⁴ + y⁴)(x² + y²)(x² − y²)

= (x⁴ + y⁴)(x² + y²)(x + y)(x − y)

Some expressions can be factored as the “difference of squares” when one of the squared terms is inside parentheses

Simplify:

[(t + 4) + 3][(t + 4) − 3]

(t + 7) (t + 1)

Watch for fractions in the expressions.

Factor out the common factors then note that the term in parentheses can be factored as the difference of squares. The remaining factors are “prime” in rational numbers.

4xy(4x² − 9y²)

4xy(2x + 3y)(2x − 3y)