Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$4 \sqrt { 5 } ( - 2 \sqrt { 5 } + 2 \sqrt { 35 } )$
A) $- 40 - 40 \sqrt { 7 }$
B) $- 40 + 8 \sqrt { 175 }$
C) $40 + 40 \sqrt { 7 }$
D) $- 40 + 40 \sqrt { 7 }$

Question

Quizplus · Accepted Answer

Use the distributive property to simplify: 
\begin{align*}
4\sqrt{5}(-2\sqrt{5}+2\sqrt{35}) &= (-8\cdot5\sqrt{5})+(8\cdot5\sqrt{7}) \
&= -40\sqrt{5}+40\sqrt{7} \
&= -40+40\sqrt{7}\sqrt{5} \
&= -40+40\sqrt{35} \
\end{align*}
Since $\sqrt{35}$ cannot be simplified further, the answer is $\boxed{	extbf{(D)}\ - 40 + 40\sqrt{7}}.$

Choose the One Alternative That Best Completes the Statement or Answers