Find the binomial that completes the factorization. w^3 + 512 = (______)(w^2 - 8w + 64)

Recognize Perfect Cube: Recognize that 512 is a perfect cube, 512 = 8^3.Use Sum of Cubes Formula: Use the sum of cubes formula: a^3 + b^3 = (a + b)(a^2 - ab + b^2).Identify a and b: Identify a = w and b = 8, since w^3 + 8^3 is the expression we have.Plug into Formula: Plug a and b into the sum of cubes formula: w^3 + 8^3 = (w + 8)(w^2 - w*8 + 8^2).Simplify Binomial and Trinomial: Simplify the binomial and trinomial: (w + 8)(w^2 - 8w + 64).

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Find the binomial that completes the factorization. $\newline$ $w^3 + 512 = (\underline{\hspace{3cm}})(w^2 - 8w + 64)$

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Algebra 2

Factor sums and differences of cubes

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Q. Find the binomial that completes the factorization.

\newline

w^3 + 512 = (\underline{\hspace{3cm}})(w^2 - 8w + 64)

Recognize Perfect Cube: Recognize that $512$ is a perfect cube, $512 = 8^3$ .
Use Sum of Cubes Formula: Use the sum of cubes formula: $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ .
Identify $a$ and $b$ : Identify $a = w$ and $b = 8$ , since $w^3 + 8^3$ is the expression we have.
Plug into Formula: Plug $a$ and $b$ into the sum of cubes formula: $w^3 + 8^3 = (w + 8)(w^2 - w\cdot8 + 8^2)$ .
Simplify Binomial and Trinomial: Simplify the binomial and trinomial: $(w + 8)(w^2 - 8w + 64)$ .