# How do you find the product of (7u+6v)(7u-6v)?

$49 {u}^{2} - 36 {v}^{2}$

#### Explanation:

In this kind of question, the "middle terms" cancel out, so the first term and final terms multiply:

$\left(7 u + 6 v\right) \left(7 u - 6 v\right)$

$7 u \times 7 u = 49 {u}^{2}$
$7 u \times - 6 v = - 42 u v$
$6 v \times 7 u = 42 u v$
$6 v \times - 6 v = - 36 {v}^{2}$

The middle terms cancel and we're left with:

$49 {u}^{2} - 36 {v}^{2}$