Answer
$t^4-32t^2+256$
Work Step by Step
Using $(a+b)(a-b)=a^2-b^2$ or the special product of the sum and difference of like terms and $(a\pm b)^2=a^2\pm2ab+b^2$ or the square of a binomial, the product of the given expression, $
(t+4)(t+4)(t-4)(t-4)
,$ is
\begin{array}{l}\require{cancel}
(t+4)^2(t-4)^2
\\\\=
[(t+4)(t-4)]^2
\\\\=
[(t)^2-(4)^2]^2
\\\\=
(t^2-16)^2
\\\\=
(t^2)^2-2(t^2)(16)+(16)^2
\\\\=
t^4-32t^2+256
.\end{array}
