• # question_answer The product of $\left( \mathbf{3}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{2}}} \right)$ and $\left( \mathbf{2}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+3}{{\mathbf{y}}^{\mathbf{2}}} \right)$ is_____. A) ${{x}^{3}}+10{{x}^{2}}{{y}^{3}}+3{{y}^{4}}$B) $3{{x}^{2}}+5{{x}^{5}}{{y}^{2}}+3{{y}^{4}}$C) $6{{x}^{5}}+10{{x}^{2}}{{y}^{3}}+3{{y}^{4}}$          D) $6{{x}^{4}}+11{{x}^{2}}{{y}^{2}}+3{{y}^{4}}$E) None of these

Explanation Option [d] is correct. $\left( 3{{x}^{2}}+{{y}^{2}} \right)\left( 2{{x}^{2}}+3{{y}^{2}} \right)=6{{x}^{4}}+9{{x}^{2}}{{y}^{2}}+2{{x}^{2}}{{y}^{2}}+3{{y}^{4}}=6{{x}^{4}}+11{{x}^{2}}{{y}^{2}}+3{{y}^{4}}$