Factoring the Difference of Squares

Factoring the Difference of Squares

How to factor the difference of squares: formula, examples, and their solutions.

Formula

a^2 - b^2 = (a + b)(a - b)

Recall (a + b)(a - b) formula.

If you switch both sides,
you get this factoring formula:
a2 - b2 = (a + b)(a - b).

Example 1

Factor the given polynomial. x^2 - 25

x2 - 25 = x2 - 52

Use x and 5 to factor it.

Example 2

Factor the given polynomial. 16a^2 - 49b^2

16a2 - 49b2 = (4a)2 - (7b)2

Use 4a and 7b to factor it.

Example 3

Factor the given polynomial. k^4 - 1

k4 - 1 = (k2)2 - 12

Use k2 and 1 to factor it.

k2 - 1 = k2 - 12

Use k and 1 to factor it again.