Bonus! Which of the following is the simplified form of (a + 3a) - 4(9 - a) ? -36 3a - 36 8a - 36 8a + 36 Answer Now

Linear Expressions Answer: A True

How can you use algebra tiles to simplify an algebraic expression? Combining Like Terms (Simplifying Algebraic Expressions) Unit 3-2 How can you use algebra tiles to simplify an algebraic expression? Example 2x + 3 + 3x +1 1 1 x x 1 x x x x 1 } } } 2x 3 3x 1 + + + Practice: You Try a) 3x +2 + 4x +3 b) x + 2x + 4x

Linear Expressions

Which figure below models the simplification of - 4x - 5 + 7x + 7 using these tiles? Answer Now

Factoring Expressions Chapter 3-- Lesson 2b Learning Objective – SWBAT: use the Distributive Property to factor expressions. Answer: -5n

Factoring Expressions using the Distributive Property When we factor an expression, we find all numbers or variables that divide into all of the parts of an expression. -Use the greatest common factor(GCF) so expression is factored completely. Example: 7x + 35 Both the 7x and 35 are divisible by 7 7(x + 5) By removing the 7 we have factored the problem Our Check: use the distributive property to see that the two expressions are equal. https://www.youtube.com/watch?v=ZDY806bPpYY

We can factor with numbers, variables, or both. Factor the following: 2x + 4y GCF of 2 and 4 is 2 2x + 4y = 2 · x + 2 · 2y factor each term by the GCF = 2(x + 2y) Distributive Property The factored expression is 2(x + 2y) 9b + 3 = -5j - 10k + 25m = 4a + 6a + 8ab = 3(3b + 1) -5(j + 2k - 5m) *Careful of your signs 2a(2 + 3 + 4b) https://www.youtube.com/watch?v=mUoD-3PbnpU

Factoring Out a Fraction       Answers: 1. 3(2b+3c) 2. -2(h+5j) 3. 4a(1+5b+3bc)

Factoring Out a Fraction       Answers: 1. 3(2b+3c) 2. -2(h+5j) 3. 4a(1+5b+3bc)

Factoring Out a Negative Number Factor -4p + 10 = -2(___ + ___) -2 times what is -4p?? 2p -2 times what is 10?? -5 Let’s go back and fill in the blanks. Practice Time Answers: 1. 3(2b+3c) 2. -2(h+5j) 3. 4a(1+5b+3bc)   https://www.youtube.com/watch?v=mUoD-3PbnpU

Try these: Factor the following expressions: 1.) 6b + 9c = 2.) -2h - 10j = 3.) 4a + 20ab + 12abc = 4.) -12y – 42 = 5) 1.5a – 4.5 = Answers: 1. 3(2b+3c) 2. -2(h+5j) 3. 4a(1+5b+3bc)

- If a regular pentagon has a perimeter of 10x + 25, what does each side equal? Answer: 2x + 5

- Closure Activity Match the algebraic expression on the left with it factored form on the right. 12x + 6 A. -6(2x – 1) 12x – 6 B. 6(2x – 1) -12x – 6 C. 6(2x + 1) -12x + 6 D. -6(2x + 1) C B Answer: -5n D A

Factor the following: 4p + 24q B 2 (2p + 12q) C 4(p + 6q) D 2 (2p + 24q) Answer: C

Factor the following: 5g + 15h B 5(g + 3h) C 5(g + 15h) D 5g (1 + 3h) Answer: B

Factor the following: 3r + 9rt + 15rx B 3r(1 + 3t + 5x) C 3r (3t + 5x) D 3 (r + 9rt + 15rx) Answer: B

Factor the following: 2v+7v+14v B 7v(2 + 1 + 2) C 7v (1 + 2) D v(2 + 7 + 14) Answer: D

Factor the following: -6a - 15ab - 18abc -3a(2 + 5b + 6bc) B 3a(2+ 5b + 6bc) C -3(2a - 5b - 6bc) D -3a (2 -5b - 6bc) Answer: A

What divides into the expression: -5n - 20mn - 10np Answer: -5n