Combining Like Terms You can only combine terms that have EXACTLY the same variable parts. Ex:1)2x + 3x 2)10n + 3n 2 + 9n 2 3)10x – 4(x 2 – 2x) = 5x

Which of the following is the simplified form of 5x x + 14 ? 1.-12x x x x – 18

Which of the following is the simplified form of a + 3a - 4(9 - a) ? a a a + 36

If you have a number outside of a set of ( ), you can distribute it to all terms inside the ( ) using multiplication. 5(7n – 2) 5 7n 35n – 10 Distributive Property – 5 2

Commutative Property To commute means to travel or move. This property says you can move or change the order of numbers in a problem without changing the result. Ex:5 + 2 = ● 4 = 4 ● 3 NOTE: Only works for addition and multiplication.

Associative Property To associate means to group. In math, we group numbers together using parentheses. This property says the way we group numbers together in a problem does not change the result. Ex:(3 + 5) + 2 = 3 + (5 + 2) (2 ● 4) ● 6 = 2 ● (4 ● 6) NOTE: Only works for addition and multiplication.

Which property would justify the following statement? 8 (2 6) = (8 2) 6 1.Associative property of multiplication 2.Distributive property 3.Commutative property of multiplication 4.Commutative property of addition

Which property would justify the following equation? 3(2x + 5y) = 6x + 15y 1.Associative property of multiplication 2.Distributive property 3.Commutative property of multiplication 4.Commutative property of multiplication

Which property would justify the following statement? 8x + 4 = 4 + 8x 1.Associative property of multiplication 2.Distributive property 3.Commutative property of multiplication 4.Commutative property of addition

Additive Identity Identity means oneself. The identity for addition always gives you the same number back when added to a number. ZERO is called the ADDITIVE IDENTITY. Ex: = = - 8

Additive Inverses Additive Inverses are two numbers that add up to the additive identity (zero). Ex:7 + (-7) = 0 So 7 and -7 are additive inverses. Opposites are additive inverses

Multiplicative Identity The identity for multiplication always gives you the same number back when a number is multiplied by it. ONE is the MULTIPLICATIVE IDENTITY. Ex:5 ● 1 = 5 -3 ● 1 = -3

Multiplicative Inverses Multiplicative Inverses are two numbers that multiply to the multiplicative identity (1). Ex:3 ● ⅓ = 1 So 3 and ⅓ are multiplicative inverses. Reciprocals are multiplicative inverses

Multiplicative Property of Zero The product of any number and zero is zero. Ex:.653 ● 0 = ● 0 = 0 Why isn’t zero the identity for multiplication?

Name the Property 1. 0  12 = 0 Multiplicative Prop. Of Zero (-6) = 0 Additive Inverse

3. 1  m = m Multiplicative Identity 4. x + 0 = x Additive Identity 5. Multiplicative Inverse

Homework Packet pgs. 5 – 8