# How do you factor 16r^2 - 25a^2 ?

Apr 25, 2018

$16 {r}^{2} - 25 {a}^{2} = \textcolor{b l u e}{\left(4 r + 5 a\right) \left(4 r - 5 a\right)}$

#### Explanation:

Remember: $\left({x}^{2} - {y}^{2}\right)$ can be factored as $\left(x + y\right) \left(x - y\right)$

Using $16 {r}^{2}$ as ${x}^{2}$ (that is using $4 r$ as $x$), and
using $25 {a}^{2}$ as ${y}^{2}$ (that is using $5 a$ as $y$)

we get
$\textcolor{w h i t e}{\text{XXX}} \left(4 r + 5 a\right) \left(4 r - 5 a\right)$

Apr 25, 2018

$\left(4 r - 5 a\right) \left(4 r + 5 a\right)$

#### Explanation:

$16 {r}^{2} - 25 {a}^{2} \text{ is a "color(blue)"difference of squares}$

$\text{which factors in general as}$

•color(white)(x)a^2-b^2=(a-b)(a+b)

$\text{here "16r^2=(4r)^2" and } 25 {a}^{2} = {\left(5 a\right)}^{2}$

$\Rightarrow a = 4 r \text{ and } b = 5 a$

$\Rightarrow 16 {r}^{2} - 25 {a}^{2} = \left(4 r - 5 a\right) \left(4 r + 5 a\right)$