Answer
$75y^{7}-12y^{2}$
Work Step by Step
From Page 301, we know that the product of a sum and difference of two terms $x$ and $y$ is given by the following equation: $(x+y)(x-y)=x^{2}-y^{2}$.
Therefore, $3y(5y^{3}+2)(5y^{3}-2)=3y((5y^{3})^{2}-2^{2})=3y(5^{2}(y^{3})^{2}-4)=3y(25y^{6}-4y)=75y^{7}-12y^{2}$.