Answer
$49-42x^4+9x^8$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the given expression, $
\left( 7-3x^4 \right)\left( 7-3x^4 \right)
$, is equivalent to
\begin{array}{l}\require{cancel}
\left( 7-3x^4 \right)^2
\\\\=
(7)^2+2(7)(-3x^4)+(-3x^4)^2
\\\\=
49-42x^4+9x^8
.\end{array}