Multiply and simplify. $( \sqrt [ 3 ] { 3 y } + 7 ) \left( \sqrt [ 3 ] { 9 y ^ { 2 } } - 7 \right)$
A) $27 y ^ { 3 } + 3 \sqrt { 49 y ^ { 2 } } - 49$
B) $3 y - 49$
C) $3 y - 7 \sqrt [ 3 ] { 3 y } + 7 \sqrt [ 3 ] { 9 y ^ { 2 } } - 49$
D) $27 y ^ { 3 } - 343$
E) $3 y - 7 \sqrt [ 3 ] { 9 y } - 343$

Question

Quizplus · Accepted Answer

Use the distributive property:
\begin{align*}
&( \sqrt [ 3 ] { 3 y } + 7 ) \left( \sqrt [ 3 ] { 9 y ^ { 2 } } - 7 ight)\
=& \sqrt [ 3 ] { 3 y } \cdot \sqrt [ 3 ] { 9 y ^ { 2 } } - 7 \sqrt [ 3 ] { 3 y } + 7 \sqrt [ 3 ] { 9 y ^ { 2 } } - 49\
=& \sqrt [ 3 ] { (3 y)^2 \cdot (9 y^2)} - 7 \sqrt [ 3 ] { 3 y} + 7 \sqrt [ 3 ] { 9 y ^ { 2 } } - 49 \
=& 27 y ^ { 3 } - 7 \sqrt [ 3 ] { 3 y} + 7 \sqrt [ 3 ] { 9 y ^ { 2 } } - 49 \
=& 3 y - 7 \sqrt [ 3 ] { 3 y} + 7 \sqrt [ 3 ] { 9 y ^ { 2 } } - 49. \
\end{align*}
Therefore, the answer is C.

Multiply and Simplify (3y3+7)(9y23−7)( \sqrt [ 3 ] { 3 y } + 7 ) \left( \sqrt [ 3 ] { 9 y ^ { 2 } } - 7 \right)(33y​+7)(39y2​−7)

Multiply and Simplify $( \sqrt [ 3 ] { 3 y } + 7 ) \left( \sqrt [ 3 ] { 9 y ^ { 2 } } - 7 \right)$