Find the indicated product. Assume the variable that appears as exponent represents positive integer. $\left( 3 x ^ { n } - 8 \right) ^ { 2 }$
A) $9 x ^ { 2 n } + 48 x ^ { n } + 64$
B) $9 x ^ { n } { } ^ { 2 } - 48 x ^ { n } + 64$
C) $9 x ^ { 2 n } - 48 x ^ { n } - 64$
D) $9 x ^ { 2 n } - 48 x ^ { n } + 64$
E) $9 x ^ { n } { } ^ { 2 } + 48 x ^ { n } - 64$

Question

Quizplus · Accepted Answer

We can use the formula $(a-b)^2 = a^2-2ab+b^2$ to expand the given expression:

\begin{align*}
(3x^n-8)^2 &= (3x^n)^2-2(3x^n)(8)+(8)^2 \
&=9x^{2n}-48x^n+64
\end{align*}

Therefore, the correct choice is (D).

Find the Indicated Product (3xn−8)2\left( 3 x ^ { n } - 8 \right) ^ { 2 }(3xn−8)2

Find the Indicated Product $\left( 3 x ^ { n } - 8 \right) ^ { 2 }$