Find the binomial that completes the factorization. u^3 - v^3 = (______)(u^2 + uv + v^2)

Identify pattern: Identify the pattern of a difference of cubes. u^3 - v^3 is a difference of cubes since both u^3 and v^3 are perfect cubes.Recall formula: Recall the formula for factoring a difference of cubes. The formula is a^3 - b^3 = (a - b)(a^2 + ab + b^2).Apply formula: Apply the formula to u^3 - v^3. Using the formula, (a - b) is the binomial we need to find, where a = u and b = v.Write binomial: Write down the binomial. The binomial that completes the factorization is (u - v).

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Find the binomial that completes the factorization. $\newline$ $u^3 - v^3 = (\underline{\hspace{3cm}})(u^2 + uv + v^2)$

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Q. Find the binomial that completes the factorization.

\newline

u^3 - v^3 = (\underline{\hspace{3cm}})(u^2 + uv + v^2)

Identify pattern: Identify the pattern of a difference of cubes. $u^3 - v^3$ is a difference of cubes since both $u^3$ and $v^3$ are perfect cubes.
Recall formula: Recall the formula for factoring a difference of cubes. $\newline$ The formula is $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ .
Apply formula: Apply the formula to $u^3 - v^3$ . Using the formula, $(a - b)$ is the binomial we need to find, where $a = u$ and $b = v$ .
Write binomial: Write down the binomial. $\newline$ The binomial that completes the factorization is $(u - v)$ .