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. 3 4 = 4 3 3 4 = 4 3 2 (5 3) = (2 5) 3 2 (5 3) = (2 5) 3 0 4 = 0 0 4 = 4

Commutative Property Add or multiply in any order w/same result. Addition: 1 + 2 = 2 + 1 a + b = b + a Multiplication: 2 • 3 = 3 • 2 b • c = c • b

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

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

Other properties Additive Identity: 3 + 0 = 3 Multiplicative Identity: 3 • 1 = 3 Additive Inverse: - 6 + 6 = 0 Multiplicative Inverse: ½ • 2 = 1 Multiplicative Property of Zero 8 • 0 = 0

Like Terms when terms have the same variable raised to the same power (or have no variable). Which are like terms? x 2x y 5y -3x 5 10x ½

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

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