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