To multiply a polynomial by a monomial, use the distributive property and the laws of exponents.

$\displaystyle{2}{{x}}^{{3}}{{y}}^{{2}}{\left({3}{{x}}^{{2}}\right)}+{2}{{x}}^{{3}}{{y}}^{{2}}{\left(-{5}{{x}}^{{2}}{{y}}^{{2}}\right)}+{2}{{x}}^{{3}}{{y}}^{{2}}{\left({4}{{y}}^{{2}}\right)}={6}{{x}}^{{5}}{{y}}^{{2}}-{10}{{x}}^{{5}}{{y}}^{{4}}+{8}{{x}}^{{3}}{{y}}^{{4}}\usepackage{cmbright}\Huge\$