Section 2-5Multiply and Divide Variable Expressions

Essential Questions

How are variable expressions simplified?

How are variable expressions evaluated?

Where you’ll see this:

Part-time job, weather, engineering, spreadsheets

Vocabulary1. Property of the Opposite of a Sum:

2. Distributive Property:

Vocabulary1. Property of the Opposite of a Sum: The negative

outside the parentheses makes everything inside it opposite

2. Distributive Property:

Vocabulary1. Property of the Opposite of a Sum: The negative

outside the parentheses makes everything inside it opposite

2. Distributive Property: Multiply each term inside the parentheses by the term outside

Example 1Simplify.

a. − 2(n − 5) b. .3(x + .7)

c. -(2ab + 9ac) d. 2x(4x + 7y )

Example 1Simplify.

a. − 2(n − 5) b. .3(x + .7)

c. -(2ab + 9ac) d. 2x(4x + 7y )

Example 1Simplify.

a. − 2(n − 5) b. .3(x + .7)

−2n

c. -(2ab + 9ac) d. 2x(4x + 7y )

Example 1Simplify.

a. − 2(n − 5) b. .3(x + .7)

−2n

c. -(2ab + 9ac) d. 2x(4x + 7y )

Example 1Simplify.

a. − 2(n − 5) b. .3(x + .7)

−2n +10

c. -(2ab + 9ac) d. 2x(4x + 7y )

Example 1Simplify.

a. − 2(n − 5) b. .3(x + .7)

−2n +10

c. -(2ab + 9ac) d. 2x(4x + 7y )

Example 1Simplify.

a. − 2(n − 5) b. .3(x + .7)

−2n +10 .3x

c. -(2ab + 9ac) d. 2x(4x + 7y )

Example 1Simplify.

a. − 2(n − 5) b. .3(x + .7)

−2n +10 .3x

c. -(2ab + 9ac) d. 2x(4x + 7y )

Example 1Simplify.

a. − 2(n − 5) b. .3(x + .7)

−2n +10 .3x +.21

c. -(2ab + 9ac) d. 2x(4x + 7y )

Example 1Simplify.

a. − 2(n − 5) b. .3(x + .7)

−2n +10 .3x +.21

c. -(2ab + 9ac) d. 2x(4x + 7y )

Example 1Simplify.

a. − 2(n − 5) b. .3(x + .7)

−2n +10 .3x +.21

c. -(2ab + 9ac) d. 2x(4x + 7y )

−2ab

Example 1Simplify.

a. − 2(n − 5) b. .3(x + .7)

−2n +10 .3x +.21

c. -(2ab + 9ac) d. 2x(4x + 7y )

−2ab

Example 1Simplify.

a. − 2(n − 5) b. .3(x + .7)

−2n +10 .3x +.21

c. -(2ab + 9ac) d. 2x(4x + 7y )

−2ab −9ac

Example 1Simplify.

a. − 2(n − 5) b. .3(x + .7)

−2n +10 .3x +.21

c. -(2ab + 9ac) d. 2x(4x + 7y )

−2ab −9ac

Example 1Simplify.

a. − 2(n − 5) b. .3(x + .7)

−2n +10 .3x +.21

c. -(2ab + 9ac) d. 2x(4x + 7y )

−2ab −9ac 8x2

Example 1Simplify.

a. − 2(n − 5) b. .3(x + .7)

−2n +10 .3x +.21

c. -(2ab + 9ac) d. 2x(4x + 7y )

−2ab −9ac 8x2

Example 1Simplify.

a. − 2(n − 5) b. .3(x + .7)

−2n +10 .3x +.21

c. -(2ab + 9ac) d. 2x(4x + 7y )

−2ab −9ac 8x2

+14xy

Dividing Variable Expressions

Dividing Variable Expressions

Divide each term in numerator by denominator

Dividing Variable Expressions

Divide each term in numerator by denominator

Rewrite as distribution

Dividing Variable Expressions

Divide each term in numerator by denominator

Rewrite as distribution

3 − x

2

Dividing Variable Expressions

Divide each term in numerator by denominator

Rewrite as distribution

3 − x

2

12i3 − x

1

Dividing Variable Expressions

Divide each term in numerator by denominator

Rewrite as distribution

3 − x

2

12i3 − x

1 12(3 − x )

Dividing Variable Expressions

Divide each term in numerator by denominator

Rewrite as distribution

3 − x

2

12i3 − x

1 12(3 − x )

32− 1

2x

Dividing Variable Expressions

Divide each term in numerator by denominator

Rewrite as distribution

3 − x

2

12i3 − x

1 12(3 − x )

32− 1

2x −

12

x + 32

Example 2Simplify. Practice both methods of division to see

which one you prefer.

a.

6x + 33

b. 10y − 5

2

Example 2Simplify. Practice both methods of division to see

which one you prefer.

a.

6x + 33

b. 10y − 5

2

6x

3+

33

Example 2Simplify. Practice both methods of division to see

which one you prefer.

a.

6x + 33

b. 10y − 5

2

6x

3+

33

2x +1

Example 2Simplify. Practice both methods of division to see

which one you prefer.

a.

6x + 33

b. 10y − 5

2

6x

3+

33

2x +1

12(10y − 5)

Example 2Simplify. Practice both methods of division to see

which one you prefer.

a.

6x + 33

b. 10y − 5

2

6x

3+

33

2x +1

12(10y − 5)

5y − 52

Example 2Simplify. Practice both methods of division to see

which one you prefer.

c.

1.6 − .8z

−8 d.

9x + 5y

7

Example 2Simplify. Practice both methods of division to see

which one you prefer.

c.

1.6 − .8z

−8 d.

9x + 5y

7

1.6−8

−.8z

−8

Example 2Simplify. Practice both methods of division to see

which one you prefer.

c.

1.6 − .8z

−8 d.

9x + 5y

7

1.6−8

−.8z

−8

−.2 + .1z

Example 2Simplify. Practice both methods of division to see

which one you prefer.

c.

1.6 − .8z

−8 d.

9x + 5y

7

1.6−8

−.8z

−8

−.2 + .1z

.1z − .2

Example 2Simplify. Practice both methods of division to see

which one you prefer.

c.

1.6 − .8z

−8 d.

9x + 5y

7

1.6−8

−.8z

−8

−.2 + .1z

.1z − .2

17(9x + 5y )

Example 2Simplify. Practice both methods of division to see

which one you prefer.

c.

1.6 − .8z

−8 d.

9x + 5y

7

1.6−8

−.8z

−8

−.2 + .1z

.1z − .2

17(9x + 5y )

97

x + 57

y

Example 3Evaluate when x = 2 and y = -4.

a. − 3(x2 +1) b. − 4 6 − y

Example 3Evaluate when x = 2 and y = -4.

a. − 3(x2 +1) b. − 4 6 − y

−3x2 − 3

Example 3Evaluate when x = 2 and y = -4.

a. − 3(x2 +1) b. − 4 6 − y

−3x2 − 3

−3(2)2 − 3

Example 3Evaluate when x = 2 and y = -4.

a. − 3(x2 +1) b. − 4 6 − y

−3x2 − 3

−3(2)2 − 3

−3(4) − 3

Example 3Evaluate when x = 2 and y = -4.

a. − 3(x2 +1) b. − 4 6 − y

−3x2 − 3

−3(2)2 − 3

−3(4) − 3

−12 − 3

Example 3Evaluate when x = 2 and y = -4.

a. − 3(x2 +1) b. − 4 6 − y

−3x2 − 3

−3(2)2 − 3

−3(4) − 3

−12 − 3

−15

Example 3Evaluate when x = 2 and y = -4.

a. − 3(x2 +1) b. − 4 6 − y

−3x2 − 3

−3(2)2 − 3

−3(4) − 3

−12 − 3

−15

−4 6 − (−4)

Example 3Evaluate when x = 2 and y = -4.

a. − 3(x2 +1) b. − 4 6 − y

−3x2 − 3

−3(2)2 − 3

−3(4) − 3

−12 − 3

−15

−4 6 − (−4)

−4 6 + 4

Example 3Evaluate when x = 2 and y = -4.

a. − 3(x2 +1) b. − 4 6 − y

−3x2 − 3

−3(2)2 − 3

−3(4) − 3

−12 − 3

−15

−4 6 − (−4)

−4 6 + 4

−4 10

Example 3Evaluate when x = 2 and y = -4.

a. − 3(x2 +1) b. − 4 6 − y

−3x2 − 3

−3(2)2 − 3

−3(4) − 3

−12 − 3

−15

−4 6 − (−4)

−4 6 + 4

−4 10

−4(10)

Example 3Evaluate when x = 2 and y = -4.

a. − 3(x2 +1) b. − 4 6 − y

−3x2 − 3

−3(2)2 − 3

−3(4) − 3

−12 − 3

−15

−4 6 − (−4)

−4 6 + 4

−4 10

−4(10)

−40

Example 3Evaluate when x = 2 and y = -4.

c. y - x

x - y

Example 3Evaluate when x = 2 and y = -4.

c. y - x

x - y

−4 − 2

2 − (−4)

Example 3Evaluate when x = 2 and y = -4.

c. y - x

x - y

−4 − 2

2 − (−4)

−6

6

Example 3Evaluate when x = 2 and y = -4.

c. y - x

x - y

−4 − 2

2 − (−4)

−6

6

66

Example 3Evaluate when x = 2 and y = -4.

c. y - x

x - y

−4 − 2

2 − (−4)

−6

6

66

1

Problem Set

Problem Set

p. 74 #1-47 odd

“Nobody got anywhere in the world by simply being content.” - Louis L'Amour