1. Warm Up 1. 3 ( x + 2 ) – 8x 3. = x 9 – ) 6p – 5p 2 ( 4 = p 4. 5 ( )2 –
Evaluate when 3 ( x + 2 ) – 8x 3. = x
ANSWER 9 – 2.
Evaluate when ) 6p –
5p 2 ( 4 = p 4.
ANSWER
108
Evaluate the expression. 3. 5 ( )2 –
ANSWER 25 4. 8 ÷ 32 • ( 5 + – )2 2
ANSWER 36

2. 1.3 Simplifying Algebraic Expressions 8/26/13

3. Vocabulary
Terms :
The parts of the expression that are separated by + or – sign.
When a term is the product of a number and a power of a variable, the number is the coefficient.
Ex. 2x or 2x3 2 is the coefficient
If the variable doesn’t have a number in front of it, the coefficient is 1.
Ex. x, x2 both have a coefficient of 1.
Coefficient :
Like terms :
Terms that have the same variable parts
Constant term :
A term that consists of just a number.
Ex: 5x + 8

4. Identify the terms in the expression . 11 – 2x 2 7x
Example 1
Identify Terms in an Expression
Identify the terms in the expression 11 –
2x 2 7x
Terms :
The parts of the expression that are separated by + or – sign.
ANSWER
Terms:
11, –
2x 2
7x, and

5. Like terms: x 2 and -3x 2 : 5 and -10 Example 2
Identify Coefficients and Like Terms
Identify the coefficients and like terms in the expression
x 2 7x – + 5
3x 2 10
ANSWER
Coefficients:1, -7, and -3.
Like terms: x 2 and -3x 2
: 5 and -10

6. 4x 3 9x – + 5x 2 x 2 9x 3 7x. – – – – More Examples 1.
Identify the terms, coefficients, and like terms in the expression
4x 3 9x – +
5x 2
x 2
9x 3
7x.
ANSWER
terms: 4x 3, x 2, x 2, 9x, 9x 3, 7x; –
coefficients: 4, 5, 1, , 9, 7 – – –
like terms: 4x 3 and - 9x 3,
- 5x 2 and x 2
- 9x and 7x

7. = (5 + 9) x = 14x Example 3 5x + 9x 9x + 5x
Simplify by Combining Like Terms
Simplify the expression. a. 5x + 9x
SOLUTION 9x + 5x a.
= (5 + 9) x
= x

8. Example 3 2x2 + 3x – x2 6x + 2x2 + – 6x x2 3x ( ) = 9x x2 + =
Simplify by Combining Like Terms
Simplify the expression. b.
2x2 + 3x – x2 6x +
Parenthesis is optional
2x2 + – 6x x2 3x ( )
Group like
terms. = 1 9x x2 + =
Important Note: When moving terms around, make sure you keep the sign that’s in front of it.

9. Example 3 4y – 7x – 12y + 3x 4y ( ) = – 12y 7x + 3x = – 8y 4x
Simplify by Combining Like Terms c. 4y – 7x –
12y + 3x 4y ( ) = –
12y 7x + 3x
Group like
terms. = – 8y 4x

10. Distributive Prop:
In general:
a(b+c) = ab + ac
multiply
multiply

11. 12 – 5x + 5 Example 4 12 – 5 ( x – 1 ) 5 12 – ( ) 1 x = – + 5x = ( ) 5
Simplify Expressions with Grouping Symbols
Simplify the expression. a. 12 – 5 ( x – 1 )
SOLUTION 5 12 a. – ( ) 1 x =
Distributive - 5
12 – 5x + 5
Group like terms. – + 5x = ( ) 5 12
CLT. – + 5x = 17

12. Example 4 4 ( 6 – x ) + 3 ( x – 8 ) – 4x 24 3x + = = ( ) 4x – 3x + 24
Simplify Expressions with Grouping Symbols b. 4 ( 6 – x ) + 3 ( x – 8 ) – 4x 24 3x + =
Distributive
property =
Group like
terms. ( ) 4x – 3x + 24 = x –

13. 7x – 3x x 1 + 8 10x – 7 11x – x + x2 – 4x2 5x – 3x2 4x 3 + ( ) 4 x 2
More Examples
Simplify the expression. 2.
ANSWER 4x 7x – 3x 3. x 1 + 8
10x –
ANSWER 7
11x – 4. x + x2 –
4x2 5x
ANSWER –
3x2 4x 5. 3 + ( ) 4 x 2
ANSWER 11 + 2x 6. x ( ) 2 6 –
ANSWER – 5x + 12

14. Homework 1.3 p.19 #9-48 X3 Remember: Pencil Only. Write heading.
Copy problems and show work.
Circle, highlight or box final answer.