How do you factor x^3 + (x + y)^3?

Jan 18, 2017

${x}^{3} + {\left(x + y\right)}^{3} = \left(2 x + y\right) \left({x}^{2} + x y + {y}^{2}\right)$

Explanation:

Here, we can use the identity ${a}^{3} + {b}^{3} = \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right)$

Hence ${x}^{3} + {\left(x + y\right)}^{3}$

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

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

= $\left(2 x + y\right) \left({x}^{2} + x y + {y}^{2}\right)$