Use a Factoring Formula to factor the expression. $$27 s ^ { 3 } - 125 t ^ { 3 }$$
A) $( 3 s - 5 t ) \left( 9 s ^ { 2 } + 15 s t + 25 t ^ { 2 } \right)$
B) $( 3 s + 5 t ) \left( 9 s ^ { 2 } - 15 s t + 25 t ^ { 2 } \right)$
C) $( 3 s - 5 t ) \left( 9 s ^ { 2 } + 16 s t + 25 t ^ { 2 } \right)$
D) $( 3 s + 5 t ) \left( 9 s ^ { 2 } - 17 s t + 25 t ^ { 2 } \right)$
E) $( 3 s - 5 t ) \left( 9 s ^ { 2 } + 17 s t + 25 t ^ { 2 } \right)$

Question

Quizplus · Accepted Answer

The expression $27 s ^ { 3 } - 125 t ^ { 3 }$ is a difference of cubes, which can be factored using the formula $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$. Here, $a = 3s$ and $b = 5t$, so the factored form is $( 3 s - 5 t ) \left( 9 s ^ { 2 } + 15 s t + 25 t ^ { 2 } \right)$.

Use a Factoring Formula to Factor the Expression 27s3−125t327 s ^ { 3 } - 125 t ^ { 3 }27s3−125t3

Use a Factoring Formula to Factor the Expression $27 s ^ { 3 } - 125 t ^ { 3 }$