Core Connections Geometry, 2013
CC
Core Connections Geometry, 2013 View details
2. Section 2.2
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Exercise 89 Page 121

Practice makes perfect
a 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 — can be combined.
2x + 8 + 6x + 5 In this case, we have two x-terms and two constants. Both the x-terms and the constants can be combined, so to simplify the expression we will rearrange it according to the Commutative Property of Addition, and then combine like terms.
2x+8+6x+5
2x+6x+8+5
8x+13
b The first step in simplifying this expression is to apply the Distributive Property.
15+3(2x-4)-4x
15+2x(3)-4(3)-4x
15+6x-12-4x
Now we can identify which, if any, terms can be combined. Remember, only like terms — constant terms or terms with the same variable — can be combined.
15 + 6x - 12 - 4x In this case, we have two x-terms and two constants. Both the x-terms and the constants can be combined, so to simplify the expression we will rearrange it according to the Commutative Property of Addition, and then combine like terms.
15+6x-12-4x
6x-4x+15-12
2x+3
c We want to simplify the expression by multiplying the binomials. To do so we will apply the Distributive Property.
(x-3)(3x+4)
3x(x-3)+4(x-3)
3x^2-9x+4(x-3)
3x^2-9x+4x-12
3x^2-5x-12
d The first step in simplifying this expression is to apply the Distributive Property.
5x(2x+7)+x(3x-5)
10x^2+35x+x(3x-5)
10x^2+35x+3x^2-5x
Now we can 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.
10x^2 + 35x + 3x^2 - 5x In this case, we have two x-terms and two x^2-terms. Both the x-terms and the x^2-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.
10x^2+35x+3x^2-5x
10x^2+3x^2+35x-5x
13x^2+30x