The Distributive Property

The distributive property is mental math strategy that can be used when

multiplying.

43 x 5 =?

Break apart the double-digit number.

43 x 5 =?

40 3+

Then multiply each part by 5.

43 x 5 =?

40 3 x 5 x 5

+

Then multiply each part by 5.

43 x 5 =?

40 3 x 5 x 5 200 15

+

Finally, sum your two products

43 x 5 =215

40 3 x 5 x 5 200 15+ = 215

+

Let’s look at another example.

53 x 6 = ?

Break apart the double-digit number.

53 x 6 = ?

Break apart the double-digit number.

53 x 6 = ?

50 3+

Multiply each part by 6.

53 x 6 = ?

50 3 x 6 x 6

+

Multiply each part by 6.

53 x 6 = ?

50 3 x 6 x 6 300 18

+

Sum the two products.

53 x 6 = 318

50 3 x 6 x 6 300 + 18 = 318

+

Example 1

5(3 + 2)

Proof: 5(3+2) = 5(5) = 25

15 + 10 = 25

D.P. with Addition

3(x + 2) =

Use the Distributive Property:

3(x) + 3(2)=

Now multiple:

3x + 6

This your answer

Practice

2(x + 5)=

2(5 + x)=

x(2 +5)=

Answers

2(x + 5)= 2x + 10

2(5 + x)= 10 + 2x

x(2 +5)= 2x + 10

D.P. with Subtraction

Example:

Apply the Distributive Property

3(1 –y)=

Multiply, and keep the subtraction sign

3(1) – 3(y)

Your answer

3 – 3y

Practice

2(x –5) =

3(5 –x) =

(x –5)3 =

Answers

2(x –5) = 2x -10

3(5 –x) = 15 -3x

(x –5)3 = 3x -15

Your Turn

• Use the distributive property to rewrite the expression without parenthesis

1. 3(x + 4)

2. - (y – 9)

3. x(x + 1)

4. 2(3x – 1)

5. (2x – 4)(-3)