Unit 3. Day 1.

Please get out paper for today’s lesson Name Date Period -------------------------------------------------------- Topic: Combining Like Terms & Distributive Property Use properties of operations to generate equivalent expressions

Combine “Like Terms”

Q: What are terms? 3𝑥−2 2 terms 3𝑥−8𝑦+5 3 terms 4 𝑚 3 −7 𝑛 2 +11𝑝−4 6 𝑎 2 𝑏 𝑐 99 𝑑 1 term

Combine “Like Terms” 4 + + 2 + 3 + 1 5

Example A: 4𝑥+3+2𝑥+2 6𝑥 + 5 4𝑥+3+2𝑥+2 4𝑥 + 3 + 2𝑥 + 2 6𝑥 + 5 We have simplified the expression by “combining like terms” Using the commutative property of addition

−4𝑥−3+2𝑥−2 −2𝑥 − 5 −4𝑥 −4𝑥 + −3 + −3 − 3 + 2𝑥 + 2𝑥 + −2 + −2 − 2 −2𝑥 Example B: −4𝑥−3+2𝑥−2 −2𝑥 − 5 −4𝑥 −4𝑥 + −3 + −3 − 3 + 2𝑥 + 2𝑥 + −2 + −2 − 2 −2𝑥 − 5 We have simplified the expression by “combining like terms” Using the commutative property of addition

Example C*: 7𝑛+10−5+11𝑛+2−8𝑛 Example D*: 12𝑚−3𝑡+2−8𝑚+ −7 −𝑡−2𝑚

Example C*: 7𝑛+10−5+11𝑛+2−8𝑛 10𝑛 + 7

Example D*: 12𝑚−3𝑡+2−8𝑚+ −7 −𝑡−2𝑚 2𝑚 2𝑚 −4𝑡 −4𝑡 −5 −5 +

− 1 2 𝑥− 3 4 + 3 8 𝑥+ 1 4 −0.6𝑥+ −2.3𝑦 +0.25𝑥−3.2+5.55𝑦 Example F*: − 1 2 𝑥− 3 4 + 3 8 𝑥+ 1 4 Example F*: Example G*: −0.6𝑥+ −2.3𝑦 +0.25𝑥−3.2+5.55𝑦

− 1 2 𝑥− 3 4 + 3 8 𝑥+ 1 4 − 1 8 𝑥 − 1 2 Example F*: − 1 2 + 3 8 − 1 2 𝑥− 3 4 + 3 8 𝑥+ 1 4 − 1 8 𝑥 − 1 2 − 1 2 + 3 8 − 8 + 8 4 3 − 1 8 − 3 4 + 1 4 −2 4 − 1 2 = = = =

−0.35𝑥 + 3.25𝑦 − 3.2 −0.6𝑥+ −2.3𝑦 +0.25𝑥−3.2+5.55𝑦 Example G*: 0 . 6 0 1 5 . 5 5 − 0 . 2 5 − 2 . 3 0 . 3 5 3 . 2 5

Distributive Property

Example H: Use the Distributive Property 6(𝑦−7) 6𝑦 + −42

Example I*: Use the Distributive Property −4(3𝑥+7) −12𝑥 + −28

Example J: Use the Distributive Property − (5−3𝑚) 1 −5 + +3𝑚

Example K: Simplify 5(𝑥 + 3) −7𝑥 + 2 −7𝑥 + 2 5𝑥 + 15 −2𝑥 + 17

Simplify − 8−3𝑛 +9+𝑛 Example L*: 6− 8−3𝑛 +9+𝑛 Example M*:

Example L*: − 8−3𝑛 +9+𝑛 + 9+𝑛 1 −8 + 3𝑛 1 1 + 4𝑛 4𝑛 +

Example M*: 6− 8−3𝑛 +9+𝑛 6 + 9+𝑛 1 −8 + 3𝑛 7 + 4𝑛