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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 96 Page 188

Practice makes perfect

a Although it may look complicated, notice that this is an application of the Distributive Property.

2x(3x-4)

Distribute 2x

2x(3x)-2x(4)

Multiply

6x^2-8x

b We want to simplify the expression by multiplying the binomials. To do so, we will apply the Distributive Property.

(x+3)(2x-5)

Distribute (2x-5)

x(2x-5)+3(2x-5)

Distribute x

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

Distribute 3

2x^2-5x+6x-15

Add terms

2x^2+x-15

c We want to simplify the expression by multiplying the binomials. To do so, we will apply the Distributive Property.

(2x+5)(2x-5)

Distribute (2x-5)

2x(2x-5)+5(2x-5)

Distribute 2x

4x^2-10x+5(2x-5)

Distribute 5

4x^2-10x+10x-25

Add terms

4x^2-25

d We want to multiply the given expression. To do so, we will apply the Distributive Property. Notice that this time we have to multiply three terms instead of two,

but the procedure is similar. We will just multiply them two at a time.

We will also add additional brackets to mark the selected pairs.

x(2x+1)(x-3) ⇕ [x(2x+1)](x-3)

[x(2x+1)](x-3)

Distribute x

[2x^2+x](x-3)

Distribute (x-3)

2x^2(x-3)+x(x-3)

Distribute 2x^2

2x^3-6x^2+x(x-3)

Distribute x

2x^3-6x^2+x^2-3x

Add terms

2x^3-5x^2-3x

Subchapter links

3.2.1 Constant Ratios in Right Triangles p.178-180

3.2.2 Connecting Slope Ratios to Specific Angles p.183-184

3.2.3 Expanding the Trig Table p.187-188

3.2.4 Expanding the Trig Table p.192-193

3.2.5 Applying the Tangent Ratio p.195-196