Exercise 47 Page 491

The first step in simplifying this expression is to identify which, if any, terms can be combined. Remember, only like terms — constant terms or terms with the same variable and the same exponent — can be combined. ( 3z^3 - 4z + 7z^2)+( 8z^2 - 6z - 5) In this case we have one z^3-term, two z^2-terms, two z-terms, and one constant. Only the z^2-terms and z-terms can be combined, so to simplify the expression we will remove parentheses, rearrange it according to the Commutative Property of Addition, and then combine like terms.

(3z^3-4z+7z^2)+(8z^2-6z-5)

RemovePar

Remove parentheses

3z^3-4z+7z^2+8z^2-6z-5

CommutativePropAdd

Commutative Property of Addition

3z^3+7z^2+8z^2-4z-6z-5

AddSubTerms

Add and subtract terms

3z^3+15z^2-10z-5