Exercise 26 Page 165

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. 1.5z^2 + 4.5 + 6z - 0.3 - 3z + z^2 In this case, we have two z^2-terms, two z-terms, and two constants. We can combine each of them. To simplify the expression we will rearrange it according to the Distributive Property to combine the like terms.

1.5z^2+4.5+6z-0.3-3z+z^2

CommutativePropAdd

Commutative Property of Addition

1.5z^2+z^2+6z-3z+4.5-0.3

IdPropMult

Identity Property of Multiplication

1.5z^2+1z^2+6z-3z+4.5-0.3

FactorOut

Factor out z^2

(1.5+1)z^2+6z-3z+4.5-0.3

FactorOut

Factor out z

(1.5+1)z^2+(6-3)z+4.5-0.3

AddSubTerms

Add and subtract terms

2.5z^2+3z+4.2