Factor by grouping.
-$$10 x ^ { 3 } - 12 x ^ { 2 } y - 25 x y ^ { 2 } + 30 y ^ { 3 }$$
A) $\left( 10 x ^ { 2 } - 5 y ^ { 2 } \right) ( x - 6 y )$
B) $\left( 2 x ^ { 2 } - 5 y \right) ( 5 x - 6 y )$
C) $\left( 2 x ^ { 2 } - 5 y ^ { 2 } \right) ( 5 x - 6 y )$
D) $\left( 2 x ^ { 2 } + 5 y ^ { 2 } \right) ( 5 x + 6 y )$

Question

Quizplus · Accepted Answer

To factor by grouping, we first split the expression into two groups: $10x^3 - 12x^2y$ and $-25xy^2 + 30y^3$. Factoring out the greatest common factor from each group gives us $2x^2(5x - 6y) - 5y^2(5x - 6y)$. Then, we factor out the common binomial factor $(5x - 6y)$, resulting in $(2x^2 - 5y^2)(5x - 6y)$, which matches choice C.

Factor by Grouping 10x3−12x2y−25xy2+30y310 x ^ { 3 } - 12 x ^ { 2 } y - 25 x y ^ { 2 } + 30 y ^ { 3 }10x3−12x2y−25xy2+30y3

Factor by Grouping $10 x ^ { 3 } - 12 x ^ { 2 } y - 25 x y ^ { 2 } + 30 y ^ { 3 }$