Factor the sum or difference of two cubes.
-$a ^ { 3 } b ^ { 3 } + 64$
A) $( a b + 4 ) \left( a ^ { 2 } b ^ { 2 } - 16 \right)$
B) $( a b - 4 ) \left( a ^ { 2 } b ^ { 2 } + 16 \right)$
C) $( a b - 4 ) \left( a ^ { 2 } b ^ { 2 } + 4 a b + 16 \right)$
D) $( a b + 4 ) \left( a ^ { 2 } b ^ { 2 } - 4 a b + 16 \right)$

Question

Quizplus · Accepted Answer

The sum of two cubes can be factored using the formula $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$. Here, $a^3b^3$ can be seen as $(ab)^3$ and $64$ as $4^3$, making the correct factorization $(ab + 4)(a^2b^2 - 4ab + 16)$.

Factor the Sum or Difference of Two Cubes a3b3+64a ^ { 3 } b ^ { 3 } + 64a3b3+64

Factor the Sum or Difference of Two Cubes $a ^ { 3 } b ^ { 3 } + 64$