# How do you factor 2a^2-32?

Apr 30, 2018

$2 {a}^{2} - 32 = 2 \left(a - 4\right) \left(a + 4\right)$

#### Explanation:

$2 {a}^{2} - 32 = 2 \left({a}^{2} - 16\right)$ (factoring out 2)
$= 2 \left(a - 4\right) \left(a + 4\right)$

^This is an identity, ${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

Apr 30, 2018

$2 \left(a + 4\right) \left(a - 4\right)$

#### Explanation:

To factor $2 {a}^{2} - 32$

Begin by factoring out 2 from each term.

$2 \left({a}^{2} - 16\right)$

${a}^{2} - 16$ is the difference of two squares and can be factored as ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

$2 \left(a + 4\right) \left(a - 4\right)$

Apr 30, 2018

$2 \left(a - 4\right) \left(a + 4\right)$

#### Explanation:

Factorize the expression $\left(2 {a}^{2} - 32\right)$ first, which will give us
$2 \left({a}^{2} - 16\right)$
But $\left({a}^{2} - 16\right)$ is a perfect square expression. Therefore it can further be factorized to
$\left({a}^{2} - 16\right)$
=${\left(a - 16\right)}^{2}$
=$\left(a - 4\right) \left(a + 4\right)$
Hence joining all them will sum up to
$\therefore 2 \left(a - 4\right) \left(a + 4\right)$