# Difference of Squares

The Difference of Squares is a way of showing how an expression in the form $$x^2 - y^2$$ can be written as the product of 2 binomials, with one as the Sum of Square Roots and the other as the Difference of Square Roots.

It can be expressed as:

$$(x + y)(x - y)$$

## Factoring Difference of Squares

1. Determine if there is a Greatest Common Factor (GCF) that can be factored out of both terms. Include the GCF for the remainder of the expression
2. Rewrite the expression in the form $$(x)^2 - (y)^2$$. Do this by finding the square root of both terms
3. Use the formula $$(a + b)(a – b)$$ to factor the rest of the expression

Example

Factor the binomial $$4x^2 - 25$$

We can rewrite the expression in the form $$(x)^2 - (y)^2$$:

$$= \sqrt{4x^2} - \sqrt{25}$$
$$= 2x - 5$$
$$= (2x)^2 - (5)^2$$

Use the formula $$(x + y)(x - y)$$ to factor the rest of the expression:

$$= (2x + 5)(2x - 5)$$

Therefore, we can determine that $$4x^2 - 25$$ expressed as a Difference of Squares is $$(2x + 5)(2x - 5)$$.

Factor the following binomials:

$$121x^2 - 9y^2$$

$$18x^2 - 32$$

$$(5c + 3)^2 - (2c + 1)^2$$

Find an algebraic expression for the area of the shaded region in factored form.