# Chapter 1 - Introduction to Algebraic Expressions - 1.8 Exponential Notation and Order of Operations - 1.8 Exercise Set: 107

$37a^2-23ab+35b^2$

#### Work Step by Step

Using $a(b+c)=ab+ac$ or the Distributive Property, the given expression, $12a^2-3ab+5b^2-5(-5a^2+4ab-6b^2)$, is equivalent to \begin{array}{l}\require{cancel} 12a^2-3ab+5b^2-5(-5a^2)-5(4ab)-5(-6b^2) \\\\= 12a^2-3ab+5b^2+25a^2-20ab+30b^2 .\end{array} By combining like terms, then this simplifies to \begin{array}{l}\require{cancel} (12a^2+25a^2)+(-3ab-20ab)+(5b^2+30b^2) \\\\= 37a^2-23ab+35b^2 .\end{array}

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