# How do you factor 2x^4y^2-32?

Jul 1, 2018

See a solution process below:

#### Explanation:

First, factor out a common term from each term in the expression:

$\left(2 \times {x}^{4} {y}^{2}\right) - \left(2 \times 16\right) \implies 2 \left({x}^{4} {y}^{2} - 16\right)$

Now, use this rule for quadratics to factor the term on the right:

${\textcolor{red}{x}}^{2} - {\textcolor{b l u e}{y}}^{2} = \left(\textcolor{red}{x} + \textcolor{b l u e}{y}\right) \left(\textcolor{red}{x} - \textcolor{b l u e}{y}\right)$

$2 \left({x}^{4} {y}^{2} - 16\right) \implies 2 \left({x}^{2} y - 4\right) \left({x}^{2} y + 4\right)$