# How do you solve by factoring and using the principle of zero products: 64v^2=36?

Jan 9, 2017

$v \in \left\{- \frac{3}{4} , \frac{3}{4}\right\}$

#### Explanation:

The zero product principle states that if $a b = 0$ then $a = 0$ or $b = 0$. Together with the special product ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$, we can solve for $v$:

$64 {v}^{2} = 36$

$\implies 64 {v}^{2} - 36 = 0$

$\implies {\left(8 v\right)}^{2} - {6}^{2} = 0$

$\implies \left(8 v + 6\right) \left(8 v - 6\right) = 0$

$\implies 8 v + 6 = 0 \mathmr{and} 8 v - 6 = 0$

$\implies 8 v = - 6 \mathmr{and} 8 v = 6$

$\implies v = - \frac{6}{8} \mathmr{and} v = \frac{6}{8}$

$\therefore v \in \left\{- \frac{3}{4} , \frac{3}{4}\right\}$