Problem 19 - Entrance Test

Expand (3p + 2q)(9p^2 - 6pq + 4q^2).

A. 27p^3 - 8q^3B. (3p + 2q)^3C. 27p^3 + 8q^3D. 27p^3 + 36p^2q + 24pq^2 + 8q^3

Correct: C

This expression matches the identity (a + b)(a^2 - ab + b^2) = a^3 + b^3. Here, a = 3p and b = 2q. So, (3p + 2q)((3p)^2 - (3p)(2q) + (2q)^2) = (3p)^3 + (2q)^3 = 27p^3 + 8q^3.