# How do you factor c^3 - 512?

May 2, 2018

$\left(c - 8\right) \left({c}^{2} + 8 c + 64\right)$

#### Explanation:

Rewrite $512 = {8}^{3}$
Then we get ${C}^{3} - {8}^{3}$
Now we can use the perfect square formula:
${a}^{3} - {b}^{3}$ = $\left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$ where $a = c$ and $b = 8$

${c}^{3} - {8}^{3}$ = $\left(c - 8\right) \left({c}^{2} + c .8 + {8}^{2}\right)$

${c}^{3} - {8}^{3}$ = $\left(c - 8\right) \left({c}^{2} + 8 c + 64\right)$

Since $\left({c}^{2} + 8 c + 64\right)$ cannot be factorized any more, the answer remains the same:

${c}^{3} - {8}^{3}$ = $\left(c - 8\right) \left({c}^{2} + 8 c + 64\right)$

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