Find the binomial that completes the factorization. t^3 + 64 = (______)(t^2 - 4t + 16)

Recognize formula: Recognize the sum of cubes formula: a^3 + b^3 = (a + b)(a^2 - ab + b^2). Here, t^3 + 64 can be written as t^3 + 4^3.Identify a and b: Identify a and b from the sum of cubes formula. a = t and b = 4.Apply formula: Apply the sum of cubes formula: t^3 + 4^3 = (t + 4)(t^2 - t*4 + 4^2).Simplify expression: Simplify the binomial and trinomial: (t + 4)(t^2 - 4t + 16).

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Find the binomial that completes the factorization. $\newline$ $t^3 + 64 = (\underline{\hspace{3cm}})(t^2 - 4t + 16)$

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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

t^3 + 64 = (\underline{\hspace{3cm}})(t^2 - 4t + 16)

Recognize formula: Recognize the sum of cubes formula: $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ . $\newline$ Here, $t^3 + 64$ can be written as $t^3 + 4^3$ .
Identify $a$ and $b$ : Identify $a$ and $b$ from the sum of cubes formula. $a = t$ and $b = 4$ .
Apply formula: Apply the sum of cubes formula: $t^3 + 4^3 = (t + 4)(t^2 - t\cdot 4 + 4^2)$ .
Simplify expression: Simplify the binomial and trinomial: $(t + 4)(t^2 - 4t + 16)$ .