Remove the parentheses by multiplying and then simplify by combining similar terms. $8 x \left( x ^ { 2 } - 4 x - 4 \right) + x \left( 7 x ^ { 2 } + 4 x - 5 \right)$
A) $15 x ^ { 3 } - 28 x ^ { 2 } - 39 x$
B) $15 x ^ { 3 } - 28 x ^ { 2 } - 37 x$
C) $15 x ^ { 3 } - 30 x ^ { 2 } - 38 x$
D) $16 x ^ { 3 } - 30 x ^ { 2 } - 37 x$
E) $16 x ^ { 3 } - 28 x ^ { 2 } - 37 x$

Question

Quizplus · Accepted Answer

First, distribute $8x$ in the first expression: $8x(x^2 - 4x - 4) = 8x^3 - 32x^2 - 32x$. Then, distribute $x$ in the second expression: $x(7x^2 + 4x - 5) = 7x^3 + 4x^2 - 5x$. Combine like terms: $8x^3 + 7x^3 = 15x^3$, $-32x^2 + 4x^2 = -28x^2$, and $-32x - 5x = -37x$. The simplified expression is $15x^3 - 28x^2 - 37x$.

Remove the Parentheses by Multiplying and Then Simplify by Combining 8x(x2−4x−4)+x(7x2+4x−5)8 x \left( x ^ { 2 } - 4 x - 4 \right) + x \left( 7 x ^ { 2 } + 4 x - 5 \right)8x(x2−4x−4)+x(7x2+4x−5)

Remove the Parentheses by Multiplying and Then Simplify by Combining $8 x \left( x ^ { 2 } - 4 x - 4 \right) + x \left( 7 x ^ { 2 } + 4 x - 5 \right)$