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Find the quadratic polynomial that completes the factorization. $\newline$ $r^3 + s^3 = (r + s)(\_\_\_\_\_)$

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Factor sums and differences of cubes

Full solution

Q. Find the quadratic polynomial that completes the factorization.

\newline

r^3 + s^3 = (r + s)(\_\_\_\_\_)

Identify Sum of Cubes: To factor $r^3 + s^3$ , we know it's a sum of cubes which factors as $(r + s)(r^2 - rs + s^2)$ .
Factorization Formula: Now, we just need to fill in the quadratic polynomial in the blank.
Complete Factorization: The quadratic polynomial that completes the factorization is $r^2 - rs + s^2$ .

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