The given polynomial is:
[tex](9v^4+2)+v^2(v^2w^2+2w^3-2v^2)-(-13v^2w^3+7v^4)[/tex]Start applying the distributive property:
[tex]\begin{gathered} 9v^4+2+v^2\times v^2w^2+v^2\times2w^3-v^2\times2v^2+13v^2w^3-7v^4 \\ 9v^4+2+v^4w^2+2v^2w^3-2v^4+13v^2w^3-7v^4 \end{gathered}[/tex]Now add the common terms:
[tex]\begin{gathered} \rightarrow(9v^4-2v^4-7v^4)+2+v^4w^2+(2v^2w^3+13v^2w^3) \\ \rightarrow0+2+v^4w^2+15v^2w \\ \rightarrow2+v^4w^2+15v^2w^3 \end{gathered}[/tex]By reordering terms the answer is:
[tex]\rightarrow v^4w^2+15v^2w^3+2[/tex]