# How do you factor 49x^2 - 16y^2?

May 28, 2016

(7x - 4y)(7x + 4y)

#### Explanation:

This is a $\textcolor{b l u e}{\text{difference of squares}}$

In general factorised as follows.

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Note: $49 {x}^{2} = {\left(7 x\right)}^{2} \text{ and } 16 {y}^{2} = {\left(4 y\right)}^{2}$

let a = 7x and b = 4y and substitute

$\Rightarrow 49 {x}^{2} - 16 {y}^{2} = \left(7 x - 4 y\right) \left(7 x + 4 y\right)$