# How do you find the product of (7u+4v)(7u-4v)?

Jan 21, 2017

$\left(7 u + 4 v\right) \left(7 u - 4 v\right) = 49 {u}^{2} - 16 {v}^{2}$

#### Explanation:

You can use the FOIL mnemonic if it helps...

$\left(7 u + 4 v\right) \left(7 u - 4 v\right) = {\overbrace{\left(7 u\right) \left(7 u\right)}}^{\text{First" + overbrace(color(red)(cancel(color(black)((7u)(-4v)))))^"Outside" + overbrace(color(red)(cancel(color(black)((4v)(7u)))))^"Inside" + overbrace((4v)(-4v))^"Last}}$

$\textcolor{w h i t e}{\left(7 u + 4 v\right) \left(7 u - 4 v\right)} = 49 {u}^{2} - 16 {v}^{2}$

Alternatively, spot that this is a difference of squares:

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

with $a = 7 u$ and $b = 4 v$

Hence:

$\left(7 u + 4 v\right) \left(7 u - 4 v\right) = {\left(7 u\right)}^{2} - {\left(4 v\right)}^{2} = 49 {u}^{2} - 16 {v}^{2}$