Multiply the expression as you would multiply polynomials. $$\left( x ^ { 17 / 2 } + y ^ { 7 / 2 } \right) ^ { 2 }$$
A) $\quad x ^ { 17 } - 2 x ^ { 17 } y ^ { 7 } + y ^ { 7 }$
B) $\quad x ^ { 17 } + x ^ { 17 } y ^ { 7 } + y ^ { 7 }$
C) $\quad x ^ { 17 } + y ^ { 7 }$
D) $\quad x ^ { 17 } + 2 x ^ { 17 / 2 } y ^ { 7 / 2 } + y ^ { 7 }$

Question

Quizplus · Accepted Answer

To multiply the expression as we would for polynomials, we use the distributive property twice: \begin{align*}
\left( x ^ { 17 / 2 } + y ^ { 7 / 2 } ight) ^ { 2 } &= \left( x ^ { 17 / 2 } ight) ^ { 2 } + 2 \left( x ^ { 17 / 2 } ight) \left( y ^ { 7 / 2 } ight) + \left( y ^ { 7 / 2 } ight) ^ { 2 } \
&= x ^ { 17 } + 2 x ^ { 17 / 2 } y ^ { 7 / 2 } + y ^ { 7 }
\end{align*}
Therefore, the answer is D.

Multiply the Expression as You Would Multiply Polynomials (x17/2+y7/2)2\left( x ^ { 17 / 2 } + y ^ { 7 / 2 } \right) ^ { 2 }(x17/2+y7/2)2

Multiply the Expression as You Would Multiply Polynomials $\left( x ^ { 17 / 2 } + y ^ { 7 / 2 } \right) ^ { 2 }$