Distributive Property

Distributive Property

OTo distribute and get rid of the parenthesis, simply multiply the number on the outside by the terms on the inside of the parenthesis.

a ca bcba

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Simplifying by Using the Distributive Property

Sometimes you may need to use the Distributive Property to simplify an algebraic expression.

The Distributive Property states: 

a(b + c) = ab + ac

Simplifying by Using the Distributive Property

To distribute and get rid of the parentheses, simply multiply the number on the outside by the terms on the inside of the parentheses.

2(x + 5) =

"two times the quantity of x plus five"

Simplifying by Using the Distributive Property

To distribute and get rid of the parentheses, simply multiply the number on the outside by the terms on the inside of the parentheses.

2(x + 5) = 2x

Simplifying by Using the Distributive Property

To distribute and get rid of the parentheses, simply multiply the number on the outside by the terms on the inside of the parentheses.

2(x + 5) = 2x + 10

We Do!

3(a - 9) -4(2x - 8)

We Do!

3(a - 9) -4(2x - 8)

We Do!

3(a - 9)

3a + (-27) 3a - 27

-8x + 32

3(a - 9) -4(2x - 8)-4(2x + (-8)) 3(a + (-9))

Distributing After Subtraction

When you distribute after subtraction, you must distribute the negative.

8c - 3(c - 5) =

Distributing After Subtraction

When you distribute after subtraction, you must distribute the negative.

8c - 3(c - 5) =

Distributing After Subtraction

When you distribute after subtraction, you must distribute the negative.

8c - 3(c - 5) = 8c -3c + 15

Distributing After Subtraction

When you distribute after subtraction, you must distribute the negative.

8c - 3(c - 5) = 8c -3c + 15

Then combine like terms!8c - 3c + 15 = 5c + 15

We Do!

16 - 4(c + 3) 3 - 5(a - 4)

We Do!

16 - 4(c + 3) 3 - 5(a - 4)

We Do!

16 - 4(c + 3)

16 - 4c - 124 - 4c

3 - 5(a - 4)

3 - 5a + 2023 - 5a

Distributing After Subtraction

8) 16 – 4(c + 3)

9) 3 – 5(a – 4)

When you distribute after subtraction, you must distribute the minus sign as part of the number being distributed.

You Try

Distributing When No Number is Present Outside the Parentheses

Sometimes you will come across an algebraic expression in which you will need to distribute in order to clear the parentheses, but there is no number there!

- (6x + 4) =

Distributing When No Number is Present Outside the Parentheses

In this case, you are looking for the opposite of the quantity 6x + 4.  To find this you can add a 1 and distribute -1.

- 1(6x + 4) =

Distributing When No Number is Present Outside the Parentheses

In this case, you are looking for the opposite of the quantity 6x + 4.  To find this you can add a 1 and distribute -1.

- 1(6x + 4) = -6x - 4

We Do!

- (5x - 9) - (2b + 6)

We Do!

-1(5x - 9) -1(2b + 6)

We Do!

-1(5x - 9)

-5x + 9

-1(2b + 6)

-2b - 6

Distributing ExamplesNo Number Outside

Parenthesis

5) - (5x – 9)

6) - (2b + 6)

To do this, add a 1 before the parenthesis and distribute -1.

You Try

Simplifying Algebraic Expressions: Overview

When you are simplifying algebraic expressions, you should do so in the following order:

1.Distribute to clear the parentheses

2.Combine like terms 

Put It All Together!

Try These:

4(b + 8) - 7b 4x - 8(2x + 3)

Put It All Together!

Try These:

4(b + 8) - 7b

4b + 32 - 7b-3b + 32

4x - 8(2x + 3)

4x - 16x - 24-12x - 24

PracticeDistributive Property

1) 8(x + 4)

2) 4(12 + 2x)

3) x(6 + 5)

4) 5 – 3(8x + 2)

5) 7(3x + 6) – 2