Question

find the quadratic polynomial that completes the factorization. $p^{3}-q^{3}=(p - q)(quad)$

Explanation:

Step1: Recall the difference of cubes formula

The formula for the difference of cubes is \(a^{3}-b^{3}=(a - b)(a^{2}+ab + b^{2})\).

Step2: Apply the formula to \(p^{3}-q^{3}\)

Here, \(a = p\) and \(b = q\). So substituting into the formula, we get \(p^{3}-q^{3}=(p - q)(p^{2}+pq+q^{2})\).

Answer:

\(p^{2}+pq + q^{2}\)