# Difference of squares

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Definition.

**The difference of squares of two expressions**is equal to product of sum of these expressions and the difference of these expressions:

a^{2} - b^{2} = (a + b)·(a - b)

## Derivation of the formula of difference of squares

The proof of the formula is very simple. To prove the formula is sufficient to multiply the expression:

(a - b)·(a + b) = a

^{2}+ ab - ba - b^{2}= a^{2}- b^{2}## Applying of difference of squares formula

Difference of squares formula convenient to use:

- to disclose the brackets
- to simplify expressions

## Examples of task

Example 1.

Expand brackets (x - 3)·(x + 3).
**Solution:** Apply the **difference of squares the formula.**

(x - 3)·(x + 3) = x

^{2}- 3^{2}= x^{2}- 9Example 2.

Expand brackets (2x - 3y^{2})·(2x + 3y

^{2}).

**Solution:** Apply the **difference of squares the formula.**

(2x - 3y

^{2})·(2x + 3y^{2}) = (2x)^{2}- (3y^{2})^{2}= 4x^{2}- 9y^{4}Example 3.

Simplify the expression ^{2}- 1

**Solution:** Apply the **difference of squares formula** in numerator.

^{2}- 1

Factoring: Some special cases
Square of the sum
Square of the difference
Difference of squares
Cube of sum
Cube of difference
Sum of cubes
Difference of cubes

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