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Find the binomial that completes the factorization. $\newline$ $w^3 - 216 = (\underline{\hspace{3em}})(w^2 + 6w + 36)$

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Factor sums and differences of cubes

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Q. Find the binomial that completes the factorization.

\newline

w^3 - 216 = (\underline{\hspace{3em}})(w^2 + 6w + 36)

Recognize Perfect Cube: Recognize that $216$ is a perfect cube, $216 = 6^3$ .
Use Difference of Cubes Formula: Use the difference of cubes formula: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ .
Substitute and Simplify: Let $a = w$ and $b = 6$ , then plug into the formula: $w^3 - 6^3 = (w - 6)(w^2 + 6w + 36)$ .
Check Multiplication: Check if the binomial $(w - 6)$ and the trinomial $(w^2 + 6w + 36)$ multiply to give the original expression $w^3 - 216$ .

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