Factor.
-$125 y ^ { 9 } - z ^ { 9 }$
A) $\left( 5 y ^ { 3 } - z ^ { 3 } \right) \left( 25 y + 5 y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$
B) $\left( 25 y ^ { 3 } + z ^ { 3 } \right) \left( 5 y ^ { 6 } + y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$
C) $\left( 25 y ^ { 3 } - z ^ { 3 } \right) \left( 5 y ^ { 6 } + y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$
D) $\left( 5 y ^ { 3 } - z ^ { 3 } \right) \left( 25 y ^ { 6 } - 5 y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$

Question

Quizplus · Accepted Answer

The expression $125 y ^ { 9 } - z ^ { 9 }$ is a difference of cubes, where $125y^9 = (5y^3)^3$ and $z^9 = (z^3)^3$. The difference of cubes formula is $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$. Applying this formula, we get $(5y^3 - z^3)(25y^6 + 5y^3z^3 + z^6)$, which matches choice A.

Factor - 125y9−z9125 y ^ { 9 } - z ^ { 9 }125y9−z9

Factor
- $125 y ^ { 9 } - z ^ { 9 }$