Chapter 5 - Section 5.3 - Polynomials and Polynomial Functions - Exercise Set - Page 279: 34

$13a^{2}+6ab-3b^{2}$

We are given the polynomial $-a^{2}+18ab-2b^{2}+14a^{2}-12ab-b^{2}$. We can simplify by combining like terms. $(-a^{2}+14a^{2})+(18ab-12ab)+(-2b^{2}-b^{2})$ $=(14a^{2}-a^{2})+6ab-(2b^{2}+b^{2})$ $=13a^{2}+6ab-(3b^{2})$ $=13a^{2}+6ab-3b^{2}$