Exercise 79 Page 51

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. 12x^2y - 8x^2y^2 + 11x^2y- 4x^3y^2- 9xy^2 In this case, we have two x^2y-terms, one x^2y^2-term, one x^3y^2-term, and one xy^2-term. Only the x^2y-terms can be combined, so to simplify the expression we will rearrange it according to the Commutative Property of Addition and then combine like terms.

12x^2y-8x^2y^2+ 11x^2y-4x^3y^2-9xy^2

CommutativePropAdd

Commutative Property of Addition

12x^2y+ 11x^2y-8x^2y^2-4x^3y^2-9xy^2

AddTerms

Add terms

23x^2y-8x^2y^2-4x^3y^2-9xy^2

The simplified expression is 23x^2y-8x^2y^2-4x^3y^2-9xy^2.