Distributive Property

Distributive Property

Lesson 6.12

How do you multiply a number by a variable?

• To multiply a number by a variable, remember there is always a 1 in front of that variable if the variable is alone. 4(x)= 4x It is like multiplying 4 times 1x

Multiple Choice

7(x)=

• 7x

• 7+x

Multiple Choice

9(2y)=

• 9 + 2y

• 18y

• 92y

• If the number or coefficient is more than 1 then you multiply that number times the number outside the parenthesis. 7(3y)= 21y In this case you multiply 7 times 3 and keep the y.

• Any number outside the parenthesis must be multiplied with the numbers inside the parenthesis. 5(2a-3)=5(2a) – 5(3)

                                                                            10a – 15 This is the answer. You can not combine 10 and -15 because 10 has an a =10a

Multiple Select

4(a + 3)

• 4a + 3

• 4 + 3

• 4a + 12

• a + 12

Multiple Choice

(b + 8)5

• b + 40
• 5b - 40
• 5b + 40
• 5b + 8

Multiple Choice

3(2c - 5)

• 6c - 15
• 6c + 15
• 6c + 15
• -6c - 15

Multiple Choice

2(c - 8)

• 2c - 16
• 2c + 16
• 2c - 8
• c - 16

How do you distribute and combine like terms?

First take care of whatever is in parenthesis then add the like terms.

For example 6(d-5) +25

First multiply what is outside of the parenthesis 6(d) - 6(5) + 25

6d - 30 + 25 Combine what is the same. We have -30+25=-5

The answer would be 6d -5 because you combined the constants -30 and 25.

What happens if you have the parenthesis at the end?

For example 9 + 3(2s + 7)

First multiply 3(2s+7)= 6s+21

Then put it together with the 9+ 6s+7

Commutative Property 9+7+6s=(9+7)+6s

16+6s or you can also say it is 6s+16

Multiple Choice

6 + 2(3y + 5)

• 16 + 23y

• 6 + 6y +5

• 11 + 6y

• 16 + 6y

Multiple Choice

4(5x + 7) - 5

• 20x + 2

• 20x + 28 - 5

• 20x + 23

• 45x + 23

Multiple Choice

8(x + 5)

• 8x + 13

• 8x + 5

• 8x + 40

• 13x

Multiple Choice

3(2c - 5)

• 6c - 15
• 6c + 15
• 6c + 15
• -6c - 15

Multiple Choice

12(3 + 4) =

• 36 + 48
• 15 + 16
• 123 + 124
• 0.84

Multiple Choice

(x - 6)4

• 24 - 4x
• 4x - 6
• x - 24
• 4x - 24

What if I have more than one variables?

Then you multiply the number outside the parenthesis with each coefficient inside. For example: 3(2x + 3y +z) = 3(2x) + 3(3y) + 3(z)=

6x + 9y + 3z this is the answer because there are no like terms.

Multiple Choice

Simplify the expression:
4(5b - 6f - c)

• 20b - 24f - 4c
• 9b - 10f - 4c
• 45b - 46f - 4c
• 20b + 24f + 4c