Remove the parentheses by multiplying and then simplify by combining similar terms. $8 x \left( x ^ { 2 } - 2 x - 8 \right) + x \left( 3 x ^ { 2 } + 8 x - 7 \right)$
A) $11 x ^ { 3 } - 8 x ^ { 2 } - 73 x$
B) $12 x ^ { 3 } - 8 x ^ { 2 } - 71 x$
C) $11 x ^ { 3 } - 10 x ^ { 2 } - 72 x$
D) $12 x ^ { 3 } - 10 x ^ { 2 } - 71 x$
E) $11 x ^ { 3 } - 8 x ^ { 2 } - 71 x$

Question

Quizplus · Accepted Answer

First, distribute $8x$ in the first expression: $8x(x^2 - 2x - 8) = 8x^3 - 16x^2 - 64x$. Then, distribute $x$ in the second expression: $x(3x^2 + 8x - 7) = 3x^3 + 8x^2 - 7x$. Combine like terms: $8x^3 + 3x^3 = 11x^3$, $-16x^2 + 8x^2 = -8x^2$, and $-64x - 7x = -71x$. The simplified expression is $11x^3 - 8x^2 - 71x$.

Remove the Parentheses by Multiplying and Then Simplify by Combining 8x(x2−2x−8)+x(3x2+8x−7)8 x \left( x ^ { 2 } - 2 x - 8 \right) + x \left( 3 x ^ { 2 } + 8 x - 7 \right)8x(x2−2x−8)+x(3x2+8x−7)

Remove the Parentheses by Multiplying and Then Simplify by Combining $8 x \left( x ^ { 2 } - 2 x - 8 \right) + x \left( 3 x ^ { 2 } + 8 x - 7 \right)$