Perform the indicated operations. $( a - b ) ( a + b ) ( a - 9 b )$
A) $a ^ { 3 } - a b ^ { 2 } - 9 a ^ { 2 } b + 9 b ^ { 3 }$
B) $a ^ { 3 } - 10 a ^ { 2 } b + 9 b ^ { 3 }$
C) $a ^ { 3 } - a b - 9 a ^ { 2 } b + 9 b ^ { 3 }$
D) $a ^ { 3 } + a b ^ { 2 } + 9 a ^ { 2 } b + 9 b ^ { 3 }$
E) $a ^ { 3 } - 10 a b ^ { 2 } + 9 b ^ { 3 }$

Question

Quizplus · Accepted Answer

First, use the difference of squares formula on $(a - b)(a + b)$ to get $a^2 - b^2$. Then, multiply this result by $(a - 9b)$ and simplify to get $a^3 - a^2b - 9ab^2 + 9b^3$, which matches choice A.

Perform the Indicated Operations (a−b)(a+b)(a−9b)( a - b ) ( a + b ) ( a - 9 b )(a−b)(a+b)(a−9b)

Perform the Indicated Operations $( a - b ) ( a + b ) ( a - 9 b )$