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Distributive Property

- And Combining
- Like Terms

THE NUMBER OUTSIDE THE PARENTHESES IS SUPPOSED TO

BE MULTIPLIED BY BOTH TERMS INSIDE THE

PARENTHESES, BUT MANY PEOPLE FORGET TO INCLUDE

MY FRIEND, THE SECOND TERM, WHEN THEY MULTIPLY

THE TERMS TOGETHER.

HAVE YOU EVER FELT LEFT OUT? IN THE DISTRIBUTIVE

PROPERTY ONE OF MY FRIENDS IN THE PARENTHESES

KNOWS EXACTLY HOW YOU FEEL.

What did I do wrong?

- Many people think this is the correct answer to

this problem - 5(x 1) 5x 1
- The way to solve this is to multiply both terms

inside the parentheses by the number outside the

parentheses. - 5(x 1) 5(x) 5(1)
- The correct answer is 5x 5

LETS SOLVE A PROBLEM

5( 3 9)

- USE THE
- DISTRIBUTIVE PROPERTY OF MULTIPLICATION
- OVER ADDITION
- BY ADDING
- (3 9)5 12 5 SO
- 5(3) 5(9) 60

Real World Examples

- Linda is planning a party for her best friend.

She buys 3 packs of cups for 1.99, 3 packs of

forks for 2.19, 3 packs of plates for 2.49, and

3 packs of knives for 2.19. - What was the cost for these party supplies?
- What would be the final cost if the store charges

6 tax?

Examples

- Modeling the Distributive Property using
- Algebra Tiles
- This 1 cm by 1 cm The area of this
- square has an area rectangle is x by 1 or
- of 1 sq. unit x sq. units

X - tile

x

1

1 - tile

1

1

Solving 5(x 1) using Distributive Property and

Algebra Tiles

5

5

5

x

1

x 1

Area 5(x 1) Area 5(x) 5(1) The

area is 5x 5 square units

Lets Practice!!

- 3(x - 2)

- Now you do some.
- 1) 4 (x 3)
- 7(x 2)
- 3(x 5)
- 5(x 3)
- 2(x 4)

3

X - 2 The product of this problem is 3x - 6

Like Terms

- Like terms have the same variable and the same

exponent. - When combining like terms, you add the

coefficients of the terms. A term with no

variable is called a constant. Two constants in

the same expression are also like terms. - In the example 12y 4y 3
- coefficient constant

Adding Like Terms

- (3 5)
- You can combine these because they are like

terms. - (x 5)
- You can not combine because they arent like

terms.

More Examples

- x 12 4x (Understood coefficient)
- (1 4)x 12 5x 12
- -(3x 7) 5x
- Distribute the negative one first, so your

problem becomes -3x 7 5x - (-3 5)x 7 2x - 7

How would you solve these problems?

- 15x 11x 3
- Combine like terms
- (15 11)x - 3 26x 3
- 12x 3y - 4x
- Unlike terms cant combine an x and a y
- (12 4)x 3y 8x 3y

Show us your stuff!!

- Simplify these expressions.
- 1) 8y 4y
- 2) 9a 4b a
- 3) 8r 2b 6r 4b
- 4) -12x 2 6x
- 5) 2(x 5) 7x
- You did great!!

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