Exercise 93 Page 86

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. 3 + 7x-( 2 + 9x) In this case, we have two x-terms and two constant terms. Both terms can be simplified, so let's use the Commutative Property of Addition to rearrange the expression and combine like terms.

3+7x-(2+9x)

FactorOutNegSign

Factor out a minus sign

3+7x-2-9x

CommutativePropAdd

Commutative Property of Addition

7x-9x+3-2

AddSubTerms

Add and subtract terms

-2x+1

In Part B, we want to simplify another expression. Let's take a look. 6-( 3x - 4) + 7x - 11 In this case, we have two x-terms and three constants. To simplify the expression we will rearrange it using the Commutative Property of Addition and then combine like terms. Let's do it!

6-(3x-4)+7x-11

FactorOutNegSign

Factor out a minus sign

6-3x+4+7x-11

CommutativePropAdd

Commutative Property of Addition

7x-3x+6+4-11

AddSubTerms

Add and subtract terms

4x-1

Finally, let's move on to the expression from Part C. 3x^2 + 10 - y^2 + 4x - 8x^2 - 5y - 8 + y^2 + 3 In this case, we have two x^2-terms, one x-term, two y^2-terms, one y-term, and three constants. We can combine the x^2-terms, y^2-terms, and the constant terms. Let's use the Commutative Property of Addition to rearrange the expression and combine like terms.

3x^2+10-y^2+4x-8x^2-5y-8+y^2+3

CommutativePropAdd

Commutative Property of Addition

3x^2-8x^2+4x-y^2+y^2-5y+10-8+3

AddSubTerms

Add and subtract terms

-5x^2+4x-5y+5

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Exercise 93 Page 86

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