Answer
$5x^4-17x^2y^2+6y^4$
Work Step by Step
Using the FOIL Method, $(a+b)(c+d)=ac+ad+bc+bd$, the given expression simplifies to
\begin{align*}
&
(5x^2-2y^2)(x^2-3y^2)
\\\\&=
5x^4-15x^2y^2-2x^2y^2+6y^4
\\\\&=
5x^4-17x^2y^2+6y^4
.\end{align*}