Perform the indicated operations and simplify. $\left( \alpha x ^ { 2 } - y ^ { 2 } \right) \left( \alpha x ^ { 2 } + y ^ { 2 } \right)$
A) $a ^ { 2 } x ^ { 2 } - y ^ { 2 }$
B) $a ^ { 2 } x ^ { 4 } + a x ^ { 2 } y ^ { 2 } - y ^ { 4 }$
C) $a ^ { 2 } x ^ { 4 } - y ^ { 4 }$
D) $a ^ { 2 } x ^ { 4 } - a x ^ { 2 } y ^ { 2 } - y ^ { 4 }$
E) $a ^ { 2 } x ^ { 4 } + y ^ { 4 }$

Question

Quizplus · Accepted Answer

Using the distributive property, we have:
\begin{align*}
\left( \alpha x ^ { 2 } - y ^ { 2 } ight) \left( \alpha x ^ { 2 } + y ^ { 2 } ight) &= (\alpha x^2)(\alpha x^2) + (\alpha x^2)(y^2) - (y^2)(\alpha x^2) - (y^2)(y^2)\
&= \alpha^2 x^4 + \alpha x^2y^2 - \alpha x^2y^2 - y^4\
&= \alpha^2 x^4 - y^4\
\end{align*}
Therefore, the answer is choice C.

Perform the Indicated Operations and Simplify (αx2−y2)(αx2+y2)\left( \alpha x ^ { 2 } - y ^ { 2 } \right) \left( \alpha x ^ { 2 } + y ^ { 2 } \right)(αx2−y2)(αx2+y2)

Perform the Indicated Operations and Simplify $\left( \alpha x ^ { 2 } - y ^ { 2 } \right) \left( \alpha x ^ { 2 } + y ^ { 2 } \right)$