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A.2 Simplifying Simplify means combine Like Terms.

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Presentation on theme: "A.2 Simplifying Simplify means combine Like Terms."— Presentation transcript:

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

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

3 Simplify 9x + 10x x + 8 – 3x – 7 8a – 2a a + 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

4 (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 + a = a = 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 = • 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

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

7 Name the Property. 36 • 1 = 36 = 15 • 9 = 1

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

9 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) = 3(2) a + b = b + a ab = ba 9

10 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

11 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=

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

13 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

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


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