Chapter 4 - Polynomials - 4.4 Addition and Subtraction of Polynomials - 4.4 Exercise Set - Page 260: 41

$-t^2-12t+13$

Removing the grouping symbols, then the given expression, $ (-9t+12)-(t^2+3t-1) $, is equivalent to \begin{array}{l} -9t+12-t^2-3t+1 .\end{array} By combining like terms, then \begin{array}{l} -t^2+(-9t-3t)+(12+1) \\\\= -t^2-12t+13 .\end{array}