# Which of the following is the correct factorization of x^{3}+8?

Which of the following is the correct factorization of ${x}^{3}+8$?
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puhnut1m
Step 1
Given expression :
${x}^{3}+8$
Formula used:
${x}^{3}+{y}^{3}=\left(x+y\right)\left({x}^{2}-xy+{y}^{2}\right)$
Step 2
Given expression ${x}^{3}+8$ can be written as ${x}^{3}+{2}^{3}$.
By applying the above formula sum of cube,
${x}^{3}+{2}^{3}=\left(x+2\right)\left({x}^{2}-2x+{2}^{2}\right)$
$=\left(x+2\right)\left({x}^{2}-2x+4\right)$
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Virginia Palmer
Step 1
Given:
${x}^{3}+8$
It can be written as :
${x}^{3}+{2}^{3}$
Step 2
Factorize :
use the formula : ${a}^{3}+{b}^{3}=\left(a+b\right)\left({a}^{2}-ab+{b}^{2}\right)$
$⇒k={x}^{3}+{2}^{3}$
$=\left(x+2\right)\left({x}^{2}-2x+4\right)$