How do you factor 2v^3-54?

Jun 19, 2016

$2 \left(v - 3\right) \left({v}^{2} + 3 v + 9\right)$

Explanation:

First you can factor:

$2 \left({v}^{3} - 27\right)$

then, because of the known identity:

${a}^{3} - {b}^{3} = \left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$,

you find:

$2 \left({v}^{3} - 27\right) = 2 \left(v - 3\right) \left({v}^{2} + 3 v + 9\right)$