# Factor the Difference of Two Squares: a^{2} - b^{2}

How to factor the difference of two squares, a^{2} - b^{2}: formula, 3 examples, and their solutions.

## Formula

### Formula

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

## Example 1

### Example

### Solution

Change x^{2} - 81 to the difference of two squares.

x^{2} is x^{2}.

-81 is -9^{2}.

x^{2} - 9^{2} is the difference of two squares.

So x^{2} - 9^{2} = (x + 9)(x - 9).

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

## Example 2

### Example

### Solution

Change 16a^{2} - 49b^{2} to the difference of two squares.

16a^{2} is (4a)^{2}.

-49b^{2} 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 x^{4} - 1 to the difference of two squares.

x^{4} is (x^{2})^{2}.

Power of a Power

-1 is -1^{2}.

(x^{2})^{2} - 1^{2} is the difference of two squares.

So (x^{2})^{2} - 1^{2} = (x^{2} + 1)(x^{2} - 1).

Change -1 to -1^{2}.

x^{2} - 1^{2} is the difference of two squares.

So x^{2} - 1^{2} = (x + 1)(x - 1).

So (x^{2} + 1)(x + 1)(x - 1) is the answer.