Factor completely.
-$50 a ^ { 4 } b - 18 b ^ { 3 }$
A) $2 b \left( 5 a ^ { 2 } + 3 b \right) \left( 5 a ^ { 2 } - 3 b \right)$
B) $2 b ( 5 a - 3 b ) ^ { 2 }$
C) Prime
D) $2 b ( 5 a + 3 b ) ^ { 2 }$

Question

Quizplus · Accepted Answer

We can factor out a common factor of $2b$, leaving:

$$2b(25a^3-9b^2)$$

Then we notice that $25a^3$ is a perfect cube and $9b^2$ is a perfect square, so we can apply the difference of cubes factorization to get:

$$2b(5a-3b)(25a^2+15ab+9b^2)$$

None of the factors can be factored further, so the final answer is:

$$\boxed{	extbf{(A)}\ 2 b \left( 5 a ^ { 2 } + 3 b ight) \left( 5 a ^ { 2 } - 3 b ight)}$$

Factor Completely 50a4b−18b350 a ^ { 4 } b - 18 b ^ { 3 }50a4b−18b3

Factor Completely $50 a ^ { 4 } b - 18 b ^ { 3 }$