Chapter R - Elementary Algebra Review - R.4 Polynomials - R.4 Exercise Set - Page 961: 47

$-y^2+5y-2$

Removing the grouping symbols and then combining like terms, the given expression, $ (8y^2-2y-3)-(9y^2-7y-1) ,$ simplifies to \begin{array}{l}\require{cancel} 8y^2-2y-3-9y^2+7y+1 \\\\= (8y^2-9y^2)+(-2y+7y)+(-3+1) \\\\= -y^2+5y-2 .\end{array}