# How do you factor x^2-9?

Mar 20, 2018

$\left(x - 3\right) \left(x + 3\right)$

#### Explanation:

${x}^{2} - 9 \text{ is a "color(blue)"difference of squares}$

$\text{and in general factorises as}$

•color(white)(x)a^2-b^2=(a-b)(a+b)

$\text{here "a=x" and } b = 3$

$\Rightarrow {x}^{2} - 9 = \left(x - 3\right) \left(x + 3\right)$

Mar 20, 2018

See a solution process below:

#### Explanation:

This is a special case of the quadratic:

${\textcolor{red}{x}}^{2} - {\textcolor{b l u e}{y}}^{2} = \left(\textcolor{red}{x} + \textcolor{b l u e}{y}\right) \left(\textcolor{red}{x} - \textcolor{b l u e}{y}\right)$

(x^2 - 9 =>

${\textcolor{red}{x}}^{2} - {\textcolor{b l u e}{3}}^{2} \implies$

$\left(\textcolor{red}{x} + \textcolor{b l u e}{3}\right) \left(\textcolor{red}{x} - \textcolor{b l u e}{3}\right)$