# How do you factor the expression 27x^3 + 343y^3?

May 9, 2016

$= \left(3 x + 7 y\right) \left(9 {x}^{2} - 21 x y + 49 {y}^{2}\right)$

#### Explanation:

$27 {x}^{3} + 343 {y}^{3}$
$= {\left(3 x\right)}^{3} + {\left(7 y\right)}^{3}$
Using the formula
${a}^{3} + {b}^{3} = \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right)$
the given expression becomes
$= \left(3 x + 7 y\right) {\left(3 x\right)}^{2} - 3 x \cdot 7 y + {\left(7 y\right)}^{2}$
$= \left(3 x + 7 y\right) \left(9 {x}^{2} - 21 x y + 49 {y}^{2}\right)$