Multiply. $( b - d ) \left( b ^ { 2 } + b d + d ^ { 2 } \right)$
A) $b ^ { 3 } + d ^ { 4 }$
B) $b ^ { 3 } + d ^ { 3 }$
C) $b ^ { 2 } - d ^ { 2 }$
D) $b ^ { 3 } - d ^ { 2 }$
E) $b ^ { 3 } - d ^ { 3 }$

Question

Quizplus · Accepted Answer

We can use the distributive property to simplify the expression. First, distribute b to each term inside the parentheses:

$$b \cdot b ^ { 2 } + b \cdot b d + b \cdot d ^ { 2 } - d \cdot b ^ { 2 } - d \cdot b d - d \cdot d ^ { 2 }$$

Next, we can combine like terms:

$$\begin{aligned}b ^ { 3 } + b ^ { 2 } d + b d ^ { 2 } - b ^ { 2 } d - b d ^ { 2 } - d ^ { 3 } & = b ^ { 3 } - d ^ { 3 } \end{aligned}$$

Therefore, the answer is choice E.

Multiply (b−d)(b2+bd+d2)( b - d ) \left( b ^ { 2 } + b d + d ^ { 2 } \right)(b−d)(b2+bd+d2)

Multiply $( b - d ) \left( b ^ { 2 } + b d + d ^ { 2 } \right)$