How do you factor the expression x^2 - 64?

Jun 19, 2018

See a solution process below:

Explanation:

This is a special form of the quadratic function:

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

Let ${\textcolor{red}{a}}^{2} = {x}^{2}$ then $\sqrt{{\textcolor{red}{a}}^{2}} = \sqrt{{x}^{2}} \to \textcolor{red}{a} = x$

Let ${\textcolor{b l u e}{b}}^{2} = 64$ then $\sqrt{{\textcolor{b l u e}{b}}^{2}} = \sqrt{64} \to \textcolor{b l u e}{b} = 8$

Substituting gives:

${\textcolor{red}{x}}^{2} - \textcolor{b l u e}{64} = \left(\textcolor{red}{x} + \textcolor{b l u e}{8}\right) \left(\textcolor{red}{x} - \textcolor{b l u e}{8}\right)$

Jun 19, 2018

$\left(x - 8\right) \left(x + 8\right)$

Explanation:

Given: ${x}^{2} - 64$.

Notice how $64 = {8}^{2}$.

$= {x}^{2} - {8}^{2}$

Use the difference of squares property, which states that ${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$. Letting $x = a , b = 8$, we get:

$= \left(x - 8\right) \left(x + 8\right)$