# How do you factor completely 169x^2 – 64?

Apr 17, 2017

See the entire solution process below:

#### Explanation:

This problem is a special form of this rule:

$\left(a + b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$ or ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

If we let $a = 13 x$ and let $b = 8$ and substitute we get:

$169 {x}^{2} - 64 = \left(13 x + 8\right) \left(13 x - 8\right)$

Apr 17, 2017

You may notice that both $169 \mathmr{and} 64$ are squares.

#### Explanation:

$= {13}^{2} \cdot {x}^{2} - {8}^{2}$

$= {\left(13 x\right)}^{2} - {8}^{2}$

We now use the special product ${A}^{2} - {B}^{2} \leftrightarrow \left(A + B\right) \left(A - B\right)$

$= \left(13 x + 8\right) \left(13 x - 8\right)$