distributive property

1. DISTRIBUTIVE PROPERTY
SECTION 1.5 PAGE25-31

2. OTHER PROPERTIES OF ADDITION & MULTIPLICATION
Commutative Property 𝑎 + 𝑏 = 𝑏 + 𝑎 𝑎𝑏 = 𝑏𝑎
Associative Property 𝑎 + 𝑏 + 𝑐 = 𝑎 + (𝑏 + 𝑐) 𝑎𝑏 𝑐 = 𝑎(𝑏𝑐)
Identity Additive identity is 0. Multiplicative identity is 1.
𝑎 + 0 = 𝑎 𝑎 ∙ 1 = 𝑎

3. DISTRIBUTIVE PROPERTY
𝑎 𝑏 + 𝑐 = 𝑎𝑏 + 𝑎𝑐
Combines addition and multiplication
𝑏 + 𝑐 𝑎 = 𝑏𝑎 + 𝑐𝑎

4. USE THE DISTRIBUTIVE PROPERTY TO REWRITE
2(4 + 𝑡)
2 ∙ 4 + 2 ∙ 𝑡
8 + 2𝑡

5. LIKE TERMS
Same variables with same powers
5𝑎 3𝑏 − 𝑎𝑏 2𝑎 4𝑎2
7𝑏 6𝑎𝑏 9𝑎2
5𝑎 , 2𝑎
3𝑏 , 7𝑏
−𝑎𝑏, 6𝑎𝑏
4𝑎2
, 9𝑎2

6. SIMPLIFY BY COMBINING LIKE TERMS
4𝑦3
+ 2𝑦 − 8𝑦 + 5
4𝑦3 − 6𝑦 + 5

7. SIMPLIFY BY COMBINING LIKE TERMS
7𝑎 + 2𝑎2 + 4 − 6𝑎2 − 2𝑎 + 2
2𝑎2 − 6𝑎2 + 7𝑎 − 2𝑎 + 4 + 2
−4𝑎2
+ 5𝑎 + 6

8. USE THE DISTRIBUTIVE PROPERTY TO SIMPLIFY
DON’T FORGET TO COMBINE LIKE TERMS
2 3𝑥 − 𝑦 + 5(𝑥 + 2𝑦)
3𝑥 − 𝑦 + 𝑥 + 2𝑦
6𝑥 − 2𝑦 + 5𝑥 + 10𝑦
11𝑥 + 8𝑦
2 ∙ 5 ∙