Factor the Difference of Two Squares: a2 - b2

How to factor the difference of two squares, a2 - b2: formula, 3 examples, and their solutions.

Formula

Formula

a2 - b2 = (a + b)(a - b)

Example 1

Example

Solution

Change x2 - 81 to the difference of two squares.

x2 is x2.
-81 is -92.

x2 - 92 is the difference of two squares.
So x2 - 92 = (x + 9)(x - 9).

So (x + 9)(x - 9) is the answer.

Example 2

Example

Solution

Change 16a2 - 49b2 to the difference of two squares.

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

(4a)2 - (7b)2 is the difference of two squares.
So (4a)2 - (7b)2 = (4a + 7b)(4a - 7b).

So (4a + 7b)(4a - 7b) is the answer.

Example 3

Example

Solution

Change x4 - 1 to the difference of two squares.

x4 is (x2)2.

Power of a Power

-1 is -12.

(x2)2 - 12 is the difference of two squares.
So (x2)2 - 12 = (x2 + 1)(x2 - 1).

Change -1 to -12.

x2 - 12 is the difference of two squares.
So x2 - 12 = (x + 1)(x - 1).

So (x2 + 1)(x + 1)(x - 1) is the answer.