Factor by grouping.
-$15 x ^ { 8 } + 6 x ^ { 4 } y ^ { 4 } + 20 x ^ { 4 } y ^ { 4 } + 8 y ^ { 8 }$
A) $\left( 3 x ^ { 4 } + 4 y \right) \left( 5 x ^ { 4 } + 2 y ^ { 8 } \right)$
B) $\left( 3 x ^ { 4 } + 4 y ^ { 4 } \right) \left( 5 x ^ { 4 } + 2 y ^ { 4 } \right)$
C) $\left( 15 x ^ { 4 } + 4 y ^ { 4 } \right) \left( x ^ { 4 } + 2 y ^ { 4 } \right)$
D) $\left( 3 x ^ { 4 } - 4 y ^ { 4 } \right) \left( 5 x ^ { 4 } - 2 y ^ { 4 } \right)$

Question

Quizplus · Accepted Answer

First, group the terms: $15x^8 + 6x^4y^4$ and $20x^4y^4 + 8y^8$. Factoring out the greatest common factor from each group gives: $3x^4(5x^4 + 2y^4)$ and $4y^4(5x^4 + 2y^4)$. Combining these gives $(3x^4 + 4y^4)(5x^4 + 2y^4)$.

Factor by Grouping 15x8+6x4y4+20x4y4+8y815 x ^ { 8 } + 6 x ^ { 4 } y ^ { 4 } + 20 x ^ { 4 } y ^ { 4 } + 8 y ^ { 8 }15x8+6x4y4+20x4y4+8y8

Factor by Grouping $15 x ^ { 8 } + 6 x ^ { 4 } y ^ { 4 } + 20 x ^ { 4 } y ^ { 4 } + 8 y ^ { 8 }$