Question

find the binomial that completes the factorization. $u^{3}+v^{3}=\left(\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \
ight)(u^{2}-uv + v^{2})$

Explanation:

Step1: Recall Sum of Cubes Formula

The sum of cubes formula is \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\).

Step2: Apply the Formula to Given Expression

In the expression \(u^3 + v^3\), we can identify \(a = u\) and \(b = v\) by comparing with the sum of cubes formula \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\). So the binomial factor should be \(u + v\).

Answer:

\(u + v\)