Factor the binomial completely.
-$32 a ^ { 4 } b - 18 b ^ { 3 }$
A) $2 b ( 4 a + 3 b ) ^ { 2 }$
B) $2 b ( 4 a - 3 b ) ^ { 2 }$
C) $2 b \left( 4 a ^ { 2 } + 3 b \right) \left( 4 a ^ { 2 } - 3 b \right)$
D) $( 8 a + 6 b ) \left( 4 a b - 3 b ^ { 2 } \right)$

Question

Quizplus · Accepted Answer

First, factor out the greatest common factor (GCF), which is $2b$, resulting in $2b(16a^4 - 9b^2)$. Recognizing $16a^4$ as $(4a^2)^2$ and $9b^2$ as $(3b)^2$, the expression inside the parentheses can be factored as a difference of squares: $2b[(4a^2)^2 - (3b)^2] = 2b(4a^2 + 3b)(4a^2 - 3b)$.

Factor the Binomial Completely 32a4b−18b332 a ^ { 4 } b - 18 b ^ { 3 }32a4b−18b3

Factor the Binomial Completely $32 a ^ { 4 } b - 18 b ^ { 3 }$