1. Warm Up
Aliens from another planet use the following symbols for addition and multiplication:
Use the codes below to figure out which symbol means add, and which means multiply.
Explain your answer. = =
2 ( ) = ( ) 3
2 ( ) = ( ) 3
= 0
= 4

2. Commutative Property Add or multiply in any order w/same result.
Addition: =
a + b = b + a
Multiplication: 2 • 3 = • 2
b • c = c • b

3. Associative Property Add or multiply in any grouping w/same result.
Addition: (3 + 2) = (5 + 3) + 2
a + (b + c) = (a + b) + c
Multiplication: 5 • (3 • 2) = (5 • 3) • 2
a • (b • c) = (a • b) • c

4. Distributive Property
use to eliminate parentheses so you can combine like terms.
Addition ( x + 2) = 4 • x • 2
a ( b + c) = a • b + a • c
Subtraction ( x - 2) = 4 • x • 2
a ( b - c) = a • b - a • c

5. Other properties Additive Identity: 3 + 0 = 3
Multiplicative Identity: • 1 = 3
Additive Inverse: = 0
Multiplicative Inverse: ½ • 2 = 1
Multiplicative Property of Zero • 0 = 0

6. Like Terms
when terms have the same variable raised to the same power (or have no variable).
Which are like terms?
x x y y x x ½

7. Combining Like Terms
adding or subtracting terms with the same variable
6y – 4y = 2y y – 4 = 2y x
5X4 – 3X X4 – 3X2

8. PRACTICE Simplify by combining like terms: 6x + 5x 12 y – 10y + 2
3x + 5x – 7x
2b – 3 a
3x + x + y + x2