Factor the expression as the sum or difference of two cubes.

Question

Quizplus · Accepted Answer

The expression is $8p^3-27q^3$, which can be factored as $(2p-3q)(4p^2+6pq+9q^2)$. The second factor is not a sum or difference of two cubes, but the first factor can be rewritten as $(\sqrt[3]{2}p-\sqrt[3]{3}q)(4p^2+2\sqrt[3]{4}pq+3q^2)$, which is a difference of two cubes (note that $2\sqrt[3]{4}=\sqrt[3]{32}=4\sqrt[3]{2}$). Therefore, the final factorization is $8p^3-27q^3=\boxed{(\sqrt[3]{2}p-\sqrt[3]{3}q)(4p^2+2\sqrt[3]{4}pq+3q^2)}$.

Factor the Expression as the Sum or Difference of Two