Answer
$-10y^{3}+2y^{2}+y+3$
Work Step by Step
The difference between $(-5+y^{2}+4y^{3})$ and $(-8-y+7y^{3})$,
after writing each polynomial in standard form
( in order of powers of y, highest first)
is
$ \begin{array}{rrrrrrr}
& 4y^{3} & +y^{2} & & -5\\
-( & 7y^{3} & & -y & -8)\\
\hline & & & & \\
= & -3y^{3} & +y^{2} & +y & +3
\end{array}$
From this, we subtract $(-y^{2}+7y^{3})$,
(writing in standard form)
$ \begin{array}{rrrrrr}
& -3y^{3} & +y^{2} & +y & +3\\
+( & 7y^{3} & -y^{2} & & )\\
\hline & & & & \\
= & -10y^{3} & +2y^{2} & +y & +3\\
& & & &
\end{array}$
