# Solve. Factor each expression. a.x^{3}+216

Solve. Factor each expression.
a.${x}^{3}+216$
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Asma Vang
Calculation:
Consider the polynomial as,
${x}^{3}+216$
Rewrite the polynomial as,
${x}^{3}+216={x}^{3}+{6}^{3}$
According to the factorized form of the sum of two cubes, ${u}^{3}+{v}^{3}=\left(u+v\right)\left({u}^{2}—uv+{v}^{2}\right)$.
${x}^{3}+216={3}^{3}+{6}^{3}$
$=\left(x+6\right)\left[{x}^{2}-x\left(6\right)+{6}^{2}\right]$
$=\left(x+6\right)\left({x}^{2}—6x+36\right)$
Therefore, the factorization of the polynomial ${x}^{3}+216$ is $\left(x+6\right)\left({x}^{2}—6x+36\right)$.