Multiply. $$( 2 p - 4 q ) ^ { 3 }$$
A) $8 p ^ { 3 } - 16 p q - 64 q ^ { 3 }$
B) $8 p ^ { 3 } - 64 q ^ { 3 }$
C) $8 p ^ { 3 } - 48 p ^ { 2 } q + 96 p q ^ { 2 } - 64 q ^ { 3 }$
D) $8 p ^ { 3 } - 32 p ^ { 2 } q + 64 p q ^ { 2 } - 64 q ^ { 3 }$

Question

Quizplus · Accepted Answer

To find $(2p - 4q)^3$, we use the binomial theorem or cube expansion formula $(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$. Substituting $a = 2p$ and $b = 4q$, we get $8p^3 - 3(2p)^2(4q) + 3(2p)(4q)^2 - (4q)^3 = 8p^3 - 48p^2q + 96pq^2 - 64q^3$.

Multiply (2p−4q)3( 2 p - 4 q ) ^ { 3 }(2p−4q)3

Multiply $( 2 p - 4 q ) ^ { 3 }$