Answer
$81p^{4}q^{2}-64t^{2}$
Work Step by Step
Using the special product $(a+b)(a-b)=a^2-b^2$ or the product of the sum and difference of like terms, the given expression, $ (9p^2q+8t)(9p^2q-8t) ,$ is equivalent to \begin{align*}
&
(9p^2q)^2-(8t)^2
\\&=
9^{1(2)}p^{2(2)}q^{1(2)}-8^{1(2)}t^{1(2)} &\left(\text{use }(a^mb^n)^p=a^{mp}b^{np}\right)
\\&=
9^{2}p^{4}q^{2}-8^{2}t^{2}
\\&=
81p^{4}q^{2}-64t^{2} .\end{align*} Hence, the expression $(9p^2q+8t)(9p^2q-8t)$ simplifies to $81p^{4}q^{2}-64t^{2}$.
