Factor.
-$$8 a ^ { 3 } - 27 b ^ { 3 }$$
A) $\left( 2 a + 3 b ^ { 2 } \right) \left( 4 a ^ { 2 } - 6 a b + 9 b ^ { 2 } \right)$
B) $( 2 a - 3 b ) \left( 4 a ^ { 2 } + 6 a b + 9 b ^ { 2 } \right)$
C) $( 8 a - 3 b ) \left( a ^ { 2 } + 6 a b + 9 b ^ { 2 } \right)$
D) $( 2 a - 3 b ) \left( 4 a ^ { 2 } + 9 b ^ { 2 } \right)$

Question

Quizplus · Accepted Answer

This is the factorization using the difference of cubes formula, which states that $$a^3-b^3=(a-b)(a^2+ab+b^2)$$ In this case, we have $8a^3-27b^3=(2a)^3-(3b)^3$, so we can apply the formula with $a=2a$ and $b=3b$ to get $$8a^3-27b^3=(2a-3b)(4a^2+6ab+9b^2).$$ Choice (B) matches this factorization.

Factor - 8a3−27b38 a ^ { 3 } - 27 b ^ { 3 }8a3−27b3

Factor
- $8 a ^ { 3 } - 27 b ^ { 3 }$