1. 1.3 Algebraic Expressions

2. Terms to know
Variable: a symbol, usually a letter, that represents one or more numbers
Algebraic Expression/Variable Expression: an expression that contains one or more variables
Evaluate: when you substitute numbers in for the variables in an expression and follow the order of operations to get an answer
Term: a number, a variable, or a product of a number and one or more variables
Coefficient: numerical factor in a term (the number in front of the variable)

3. What is the Order of Operations ?
PEMDAS
P – Parenthesis first
E – Exponent next
M Multiplication and Division
D from left to right
A Addition and Subtraction
S from left to right  
= 15

4. Evaluating an Algebraic Expression
White Boards
2. Evaluate 3x – 4y + x – y for x = 4 and y = –2. = 3(4) – 4(–2) + (4) – (–2) = 12 – (–8) + 4 – (–2) = – (–2) = 24 – (–2) = 26

5. Properties for Simplifying Algebraic Expressions
Let a, b, and c represent real numbers.
Definition of Subtraction
a – b = a + (–b)
Definition of Division
a ÷ b = = a  , b ≠ 0
Distributive Property for Subtraction
a(b – c) = ab – ac
Multiplication by 0
0  a = 0
Multiplication by -1
–1  a = –a
Opposite of a Sum
–(a + b) = –a + (–b)
Opposite of a Difference
–(a – b) = b – a
Opposite of a Product
–(ab) = –a  b = a  (–b)
Opposite of an Opposite
–(–a) = a

6. Simplifying Algebraic Expressions
“Like terms”:
Terms that have the same variables raised to the same power (+/- coefficients, keep variables the same) =
Ex. 3
Ex. 4 = =

7. Evaluating Algebraic Expressions
Simplify First =
4(4) – 5(-2)
Substitute Values
= 16 – (-10)
= 26

8. White Boards
6. Evaluate
for
7. Evaluate
for