Factor by grouping.
-$6 x ^ { 10 } - 9 x ^ { 5 } y ^ { 3 } + 8 x ^ { 5 } y ^ { 3 } - 12 y ^ { 6 }$
A) $\left( 3 x ^ { 5 } - 4 y ^ { 3 } \right) \left( 2 x ^ { 5 } + 3 y ^ { 3 } \right)$
B) $\left( 6 x ^ { 5 } + 4 y ^ { 3 } \right) \left( x ^ { 5 } - 3 y ^ { 3 } \right)$
C) $\left( 3 x ^ { 5 } + 4 y ^ { 3 } \right) \left( 2 x ^ { 5 } - 3 y ^ { 3 } \right)$
D) $\left( 3 x ^ { 5 } + 4 y \right) \left( 2 x ^ { 5 } - 3 y ^ { 6 } \right)$

Question

Quizplus · Accepted Answer

The expression can be grouped and factored as follows: $6x^{10} - 9x^5y^3 + 8x^5y^3 - 12y^6$ becomes $(6x^{10} + 8x^5y^3) + (-9x^5y^3 - 12y^6)$. Factoring out common terms gives $2x^5(3x^5 + 4y^3) - 3y^3(3x^5 + 4y^3)$, which can be further factored as $(3x^5 + 4y^3)(2x^5 - 3y^3)$.

Factor by Grouping 6x10−9x5y3+8x5y3−12y66 x ^ { 10 } - 9 x ^ { 5 } y ^ { 3 } + 8 x ^ { 5 } y ^ { 3 } - 12 y ^ { 6 }6x10−9x5y3+8x5y3−12y6

Factor by Grouping $6 x ^ { 10 } - 9 x ^ { 5 } y ^ { 3 } + 8 x ^ { 5 } y ^ { 3 } - 12 y ^ { 6 }$