Exercise 22 Page 287

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

5.1.1 Sine and Cosine Ratios p.281-282

5.1.2 Selecting a Trig Tool p.286-287

5.1.3 Inverse Trigonometry p.290-291

5.1.4 Trigonometric Applications p.294-295

Exercise 22 Page 287

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