A.2 Simplifying Simplify means combine Like Terms. Like Terms mean the terms that share the same variable(s) with the same powers. Examples:

Practice with Like Terms 1. 4x + 5x 2. 3x – 2x 3. 12x3 – 4x3 + 5 4. 3x + 2y – x + 7y + 1 5. 3y3 + 3y + 4y3 – 2y + 6

Simplify 9x + 10x 9. 12x + 8 – 3x – 7 8a – 2a 10. 3a + 7b + 5c + a – 2c 3x + 9y + x – 3y 8a – 2a + 12b – 4b + 4 8x – 3x + 4x 15b – 12b – 2b c + 7c – 2 12x2 + 2b – 11x2 + 6b

(A.2) Properties 0 + a = a 0 + 5 = 5 Additive identity : Key Word: No Change (+0) Because adding 0 does not change the value. Examples: a + 0 = a 5 + 0 = 5 0 + a = a 0 + 5 = 5

Multiplication Properties Multiplicative Identity: Key Word: No Change (•1), because… multiplying by 1 does not change the value. Examples: 13 • 1 = 13 a • 1 = a 1 • 13 = 13 1 • a = a Multiplicative Property of Zero: The product of any number and zero is always 0. 4 • 0 = 0 a • 0 = 0 0 • 4 = 0 0 • a = 0

Multiplication Properties Multiplicative Inverse: Key Word: Flip the Fraction For any number, if you multiply by the reciprocal, the result it 1. Examples:

Name the Property. 36 • 1 = 36 0 + 15 = 15 • 9 = 1

U try to name the property, and solve for n 1 • 14 = 14 6 • 1/6 = 1 0 + 8 = 8

Commutative Property The order in which you add or multiply numbers does not affect their sum or product. Key Words: Order Changes Examples: 2 + 3 = 3 + 2 2(3) = 3(2) a + b = b + a ab = ba 9

Associative Property The way you group three or more numbers when adding or multiplying does not change their sum or product. Key Words: Groups Change Examples: (2 + 3) + 4 = 2 + (3 + 4) 10

Distributive Property For any numbers a, b, and c. Distributive Property – a(b + c) = ab + ac Key Word: Distribute a(b – c) = ab – ac (b + c)a = ab + ac (b – c)a = ab – ac Example: 2(3x + 4)= (3x – 4) 2=

Properties Review Identify the following properties. (x + 3)2 = 2x + 6 7. 5(4 • 6) = 5(6 • 4) 3x + 6 = 6 + 3x 8. 0 + ½ = ½ s + 0 = s 9. 4x – 8 = 4(x – 2) 5 (4 • 6) = (5 • 4)6 4 • 1 = 4 ¼ • 4 = 1

Distributive Property with variables Rewrite using the distributive property. a) 8(9 + x) b) (2y2 – 6)4 c) 6(2x – 4) d) (3x + 4y)5

Simplify an Expression a) 3c + 5(2 + c) b) 8(2b + 4) + 7b 14