CHAPTER 2.5

The Distributive Property & Combining

Like Terms

Vocabulary:

terms: parts of an expression that are added together

coefficient: number part of a term with a variable part

like terms: have identical variable partsconstant term: a term that has no

variable

Example 3 Identify parts of an expression

Identify the terms, like terms, coefficients, and constant terms of the expression 3x 4 6x 2.– – +

SOLUTIONWrite the expression as a sum: 6x–( )4 )3x –(+ + + 2

Terms: 6x,–3x, 4,– 2

Like terms: 3x and 6x;– 4 and 2–

Coefficients: 3, 6–

Constant terms: 4,– 2

The Distributive Property

A (B + C) = AB + AC-A (B + C) = -AB - AC

The distributive property says that a number next to the parentheses can be multiplied by each number inside the parentheses.

Example

5(3) + 5(4)

= 15 + 20

= 35

5 (3 + 4) =

4(-1) + 4(3)

= -4 + 12

= 8

4 (-1+ 3) =

Example

3(5) + 3(6)

= 15 + 18

= 33

3 (5 + 6) =

2(-1) + 2(5)

= -2 + 10

= 8

2 (-1 + 5) =

3 (x + 2)

x 1 1x 1 1x 1 1

3(x) + 3(2)=

3x + 6=

Example

2 (x2 + 2x - 2) 2(x2) + 2(2x)=

2x2 + 4x=

Example

2(2)-

x2

x2

xx

xx

-1-1

-1-1

- 4

Two practice problems

1. = 3 (2x2) – 3(10x) + 3(7)

2. = 6x2 – 30x + 21

1. = m (6x2) + m(4x) – m(12)

2. = 6x2m + 4xm – 12m

3 (2x2 – 10x + 7) =

m (6x2 + 4x – 12) =

Notes

When multiplying by a negative number, use the distributive property and follow the rules for multiplying integers

+ • + = + or - • - = + (same signs = positive)

- • + = - or + • - = - (opposite signs = negative)

Example

-3(2x) + -3(4)

= -6x + -12

-3 (2x + 4)=

-2(-1x) ̶ -2(7)

= 2x ̶̶ -14

= 2x + 14

-2 (-x – 7) =

Example

-(-4x) + -(2)

= 4x + -2

- (-4x + 2) =

-12(x) ̶ -12(4)

= -12x ̶̶ -48

= -12x + 48

-12 (x – 4)=

DISTRIBUTIVE PROPERTY

Whiteboard Races!!!

1. We are in teams of 3 or 4. 2. Mr. Becker will give us a problem and EVERYONE

will work it out silently on their boards for 30 seconds. 3. When Mr Becker says “team time”, we have an

additional minute to compare our problems with our teammates

4. We will only get a point if everyone has the answer correct .

5. When Mr Becker says boards up, all boards go up. Any team who does not have all boards up with correct answers cannot score a point.

Problem 1

2 (x + 3)

2 (x + 3)

2x + 6

Problem 2

3 (4 + 5x)

3 (4 + 5x)

12 + 15x

Problem 3

-4(2x – 7)

-4(2x – 7)

-8x + 28

Problem 4

-2(8 + 4x)

-2(8 + 4x)

-16x – 8

Problem 5

- (3x – 5)

- (3x – 5)

-3x + 5

Problem 6

- (8 + 12x)

- (8 + 12x)

-8 – 12x

Problem 7

9 + 5(4x + 4)

9 + 5(4x + 4)

20x + 29

Problem 8

2x + 3(5 + 4x)

2x + 3(5 + 4x)

15 + 14x

Problem 9

2x + 3 – (x + 5)

2x + 3 – (x + 5)

x – 2

Problem 10

3x – (2x + 5) + 8

3x – (2x + 5) + 8

x + 3

Problem 11

4x – 2(3x – 3)

4x – 2(3x – 3)

-2x + 6

Problem 12

7x + 3 – (6x + 5)

7x + 3 – (6x + 5)

x – 2

Problem 13

a (2x + 3)

a (2x + 3)

2xa + 3a

NOW YOU’RE AT BAT. YOU ARE SITTING

SILENTLY WHILE I HAND OUT THE WORKSHEET.

THE END!