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Core Connections Integrated II, 2015
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Core Connections Integrated II, 2015 View details
2. Section 3.2
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Exercise 75 Page 179

Practice makes perfect
a We want to simplify the expression by multiplying the binomials. To do so we will apply the Distributive Property.
(2x+1)(3x-2)
Distr

Distribute (3x-2)

2x(3x-2)+1(3x-2)
Distr

Distribute 2x

6x^2-4x+1(3x-2)
IdPropMult

Identity Property of Multiplication

6x^2-4x+3x-2
AddTerms

Add terms

6x^2-x-2
b To simplify the expression by multiplying a binomial by a trinomial, we will apply the Distributive Property.
(2x+1)(3x^2-2x-5)
Distr

Distribute (2x+1)

3x^2(2x+1)-2x(2x+1)-5(2x+1)
Distr

Distribute 3x^2

6x^3+3x^2-2x(2x+1)-5(2x+1)
Distr

Distribute - 2x

6x^3+3x^2-4x^2-2x-5(2x+1)
Distr

Distribute - 5

6x^3+3x^2-4x^2-2x-10x-5
AddTerms

Add terms

6x^3-x^2-12x-5
c We want to simplify the expression by multiplying the binomials. To do so we will apply the Distributive Property.
(3y-8)(- x+y)
Distr

Distribute (- x+y)

3y(- x+y)-8(- x+y)
Distr

Distribute 3y

- 3xy +3y^2-8(- x+y)
Distr

Distribute - 8

- 3xy +3y^2+8x-8y
CommutativePropAdd

Commutative Property of Addition

3y^2 - 3xy +8x-8y
d We want to simplify the expression by multiplying the binomials. To do so we will apply the Distributive Property.
(x-3y)(x+3y)
Distr

Distribute (x-3y)

x(x-3y)+3y(x-3y)
Distr

Distribute x

x^2-3xy+3y(x-3y)
Distr

Distribute 3y

x^2-3xy+3xy-9y^2
AddTerms

Add terms

x^2-9y^2
Subchapter links expand_more
arrow_right 3.2.1 Constant Ratios in Right Triangles p.178-180
72
Constant Ratios in Right Triangles 73 (Page 179)
Constant Ratios in Right Triangles 74 (Page 179)
Constant Ratios in Right Triangles 75 (Page 179)
Constant Ratios in Right Triangles 76 (Page 179)
Constant Ratios in Right Triangles 77 (Page 180)
arrow_right 3.2.2 Connecting Slope Ratios to Specific Angles p.183-184
Connecting Slope Ratios to Specific Angles 83 (Page 183)
Connecting Slope Ratios to Specific Angles 84 (Page 184)
Connecting Slope Ratios to Specific Angles 85 (Page 184)
Connecting Slope Ratios to Specific Angles 86 (Page 184)
Connecting Slope Ratios to Specific Angles 87 (Page 184)
Connecting Slope Ratios to Specific Angles 88 (Page 184)
arrow_right 3.2.3 Expanding the Trig Table p.187-188
Expanding the Trig Table 93 (Page 187)
Expanding the Trig Table 94 (Page 187)
Expanding the Trig Table 95 (Page 187)
Expanding the Trig Table 96 (Page 188)
Expanding the Trig Table 97 (Page 188)
Expanding the Trig Table 98 (Page 188)
arrow_right 3.2.4 Expanding the Trig Table p.192-193
Expanding the Trig Table 105 (Page 192)
Expanding the Trig Table 106 (Page 192)
Expanding the Trig Table 107 (Page 192)
Expanding the Trig Table 108 (Page 192)
Expanding the Trig Table 109 (Page 193)
Expanding the Trig Table 110 (Page 193)
arrow_right 3.2.5 Applying the Tangent Ratio p.195-196
Applying the Tangent Ratio 113 (Page 195)
Applying the Tangent Ratio 114 (Page 196)
Applying the Tangent Ratio 115 (Page 196)
Applying the Tangent Ratio 116 (Page 196)
Applying the Tangent Ratio 117 (Page 196)
Applying the Tangent Ratio 118 (Page 196)