Question

which expression is equivalent to the given polynomial expression? $({9v}^{4} + 2) + {v}^{2} ( {v}^{2} {w}^{2} + 2 {w}^{3} - 2 {v}^{2} ) - ( - 13 {v}^{2} {w}^{3} + 7 {v}^{4} )$

Answer 1

The given polynomial is:

$(9v^4+2)+v^2(v^2w^2+2w^3-2v^2)-(-13v^2w^3+7v^4)$

Start applying the distributive property:

$\begin{gathered} 9v^4+2+v^2\times v^2w^2+v^2\times2w^3-v^2\times2v^2+13v^2w^3-7v^4 \\ 9v^4+2+v^4w^2+2v^2w^3-2v^4+13v^2w^3-7v^4 \end{gathered}$

Now add the common terms:

$\begin{gathered} \rightarrow(9v^4-2v^4-7v^4)+2+v^4w^2+(2v^2w^3+13v^2w^3) \\ \rightarrow0+2+v^4w^2+15v^2w \\ \rightarrow2+v^4w^2+15v^2w^3 \end{gathered}$

By reordering terms the answer is:

$\rightarrow v^4w^2+15v^2w^3+2$