# How do you find the product (5r+7)(5r-7)?

Feb 16, 2017

$\left(5 r + 7\right) \left(5 r - 7\right) = 25 {r}^{2} - 49$

#### Explanation:

$\textcolor{red}{\left(x - a\right) \left(x + a\right) = {x}^{2} - {a}^{2}}$
$\left(5 r + 7\right) \left(5 r - 7\right) = {\left(5 r\right)}^{2} - {\left(7\right)}^{2} = 25 {r}^{2} - 49$

$\text{or}$

$\left(5 r + 7\right) \left(5 r - 7\right) = 5 r \cdot 5 r - 5 r \cdot 7 + 7 \cdot 5 r - 7 \cdot 7$

$\left(5 r + 7\right) \left(5 r - 7\right) = 25 {r}^{2} \cancel{- 35 r} \cancel{+ 35 r} - 49$

$\left(5 r + 7\right) \left(5 r - 7\right) = 25 {r}^{2} - 49$