How do you factor completely 2x^2 - 32?

Apr 26, 2016

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

Explanation:

Separate out the common scalar factor $2$ then use the difference of squares identity:

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

with $a = x$ and $b = 4$ as follows:

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