Definition Of Distributive Property:

A property indicating a way in which multiplication is applied to basic operations of two or more variables in which each term inside a set of parentheses can be multiplied by a number outside the parentheses.

EXAMPLE: 3(x+5)

VOCAB WORDS!

Coefficient:

A number or symbol multiplied with a variable or an unknown quantity in an algebraic term, (example 4 in the term 4x, or x in the term x(3 + 7).)

Terms:

A number (constant term), a variable (algebraic term), or a combination of numbers or variables that are added to form an expression.

Given the problem 2x + 5, the terms are 2x and 5.

Given the problem 2x – 5, the terms are 2x and –5.

Definition For Like Terms

Like Terms:

Terms in an expression that have the same variable raised to the same power.

(example:)

4x and 3x = like terms

8x and 2 squared= NON-like terms

Here is a better example of like terms and unlike terms...

Simplify:

Solve, or to work the problem until there are no other smaller answers until there are no more numbers

**Distributive Property:**

EXAMPLE:

EXAMPLE:

2(5x + 3)

2

(

5x + 3

)

=

2

(

5x

)

+

2

(

3

)

= 10x + 6

step 1.) Take the number to the left.

step 2.) Take the number then times it by each number inside the parenthesis.

(don't forget to add your variable!)

step 3.) Get you answer!

Combining Like Terms

EXAMPLE:

3x

+

2y

+

4x

+

8

+

y

7x

+

3x

+

8

2y + y = 3y

4x + 3x = 7x

**(**

**)**

BY: ALEX LAUQUAN

Now we will use the distributive property first, then combine like terms second.

1. Simplify 6(5 + n) – 2n.

6(5 + n) – 2n

distributive Property

6

(5) +

6

(n) – 2n

multiply

30 + 6n - 2n

Combine coefficients 6n – 2n = 4n

30 + 4n

**Now you guys try a couple:**

Simplify:

1.) 4(3x + 6) + 7x

2.) 6(x + 5) + 3x

3.) 5(2x - 3) + 4x

4.) 7(5n - 1) - 2n

5.) 9c + 12c + 16c - 10a + 16a

6.) 2b - 17a + 18b - 10a - 17a + 10b

BONUS:

-7(22x + 17) + 39x + =6 - 4 + 3 - 54x +7

**HOMEWORK OR IN SCHOOL WORK: Distributive Property And Combining Like Terms**

Use Distributive Property to simplify each expression.

1.) 7 (1 - 8n)

2.) -8 (b + 3) 6.) -6 (3x - 9)

3.) -6 (9 - 9c) 7.) -10 (a + 2)

4.) -9 (n + 6) 8.) -4 (4 + 3p)

5.) 5(n - 10) - 9

Use Distributive Property AND Combining Like Terms to simplify each expression.

9.) 6 (x + 2) - 2 11.) 7 (3 - 6v)

10.) 4n (7 - 6n) 12.) -5 (a - 6) + 2a

Use Distributive Property AND Combining Like terms to simplify each expression.

13.) 7 (5n - 8) + 6 (4 + 6n) 15.) -4 (1 - 8n) - 4 (8n + 4)

14.) -3 (a + 2) - 3 (5a + 7) 16.) 5 (-3p + 7) + 5 (p - 1)

If you want to try:

17.) 9 (m + 8) + 11 (3m + 4)

18.) 7 (-12x - 3) + 10 (6x + 7)

Use Distributive Property to simplify each expression.

1.) 7 (1 - 8n)

2.) -8 (b + 3) 6.) -6 (3x - 9)

3.) -6 (9 - 9c) 7.) -10 (a + 2)

4.) -9 (n + 6) 8.) -4 (4 + 3p)

5.) 5(n - 10) - 9

Use Distributive Property AND Combining Like Terms to simplify each expression.

9.) 6 (x + 2) - 2 11.) 7 (3 - 6v)

10.) 4n (7 - 6n) 12.) -5 (a - 6) + 2a

Use Distributive Property AND Combining Like terms to simplify each expression.

13.) 7 (5n - 8) + 6 (4 + 6n) 15.) -4 (1 - 8n) - 4 (8n + 4)

14.) -3 (a + 2) - 3 (5a + 7) 16.) 5 (-3p + 7) + 5 (p - 1)

If you want to try:

17.) 9 (m + 8) + 11 (3m + 4)

18.) 7 (-12x - 3) + 10 (6x + 7)

Which ones are like terms?

4x:7x

3y:7b

1/3xy:-2xy

24b:24c

YES

NO

YES

NO