1-7 The Distributive Property

Objective: To use the distributive property to simplify expressions.

Drill #9

Solve each expression using the order operations. Name the property illustrated by each step.

1.

2.

313)523(2

)3412(56126

Name the property*

1. If a = 2 + 1 and 2 + 1 = 3 then a = 3

2. If x = y then y = x

3. 6 = 6

4. If x + 7 = 5x + 2 and x = 10 then 10 + 7 = 5(10) + 2

The Distributive Property**

Definition: For any numbers a, b, and c,

a ( b + c ) = ab + ac and ( b + c ) a = ba + ca;

a ( b – c ) = ab – ac and ( b – c ) a = ba – ca;

Example:10 ( x + 2) = 10x + 10(2) = 10x + 20

Using the distributive property*

We can use the distributive property to multiply big numbers easier…

Example:What is 14 (98) ?

solution: 14 (100 – 2) 1400 – 28

1372

Find the following values using the distributive property*:

1. 16 (103)

2. 26 (999)

3. 11(1001)

4. 14 ( 111)

Term (II) **

Definition: a number, a variable, or a product of numbers and variables.

Example: Name each term:

5x – 3xy + 2 = 65 – 32 + 2x – 2xy + 3y

Coefficient**

Definition: The numerical factor of a variable expression.

The number in front of a variable term…Its what’s left when you remove all the variables

Example:5x 5 -6xy -6 30xyz 30

Name the coefficient*

1. 10xy

2. 15y – 16x

3. 0x

Like Terms**

Definition: Terms that contain the same variables, with corresponding variables to the same power.

Example: In the expression 3xy + y – xy + 3x + 4y

Combining Like Terms

1. When you combine like terms, find variables that have the same letters (to the same powers). Group them together…

Remember to keep the negative signs with variables that are being subtracted…

2. Add the coefficients of the like terms together. The variable part of the expression remains the same.

Like Terms Example

xxxyxxyx 243453 22

)35()24()43( 22 xyxyxxxx

xyxx 862

Equivalent Expressions**

Definition: Algebraic expressions that denote the same number, or share the same simplest form.

Example: 2x – 3 + 4x and 6x – 3 are equivalent expressions.

Simplest Form

Definition: An expression is in simplest form when it is replaced by an equivalent expression having no like terms or parenthesis.

Example: Write 5x + 3(x + 2) in simplest form

8x + 2

Simplest Form*

1. Remove parenthesis. (Distribute)2. Identify like terms and combine. Simplify each expression:

33

2424

24

234

aa

wwww