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

2. Linear Expressions
Answer: A True

3. 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 x +1 1 1 x x 1 x x x x 1 } } } 2x 3 3x 1 + + +
Practice: You Try
a) 3x x b) x + 2x + 4x

4. Linear Expressions

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

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

7. 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.

8. 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( b)

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

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

11. 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)

12. 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)

13. -
If a regular pentagon has a perimeter of 10x + 25, what does each side equal?
Answer: 2x + 5

14. -
Closure Activity
Match the algebraic expression on the left with it factored form on the right.
12x A. -6(2x – 1)
12x – B. 6(2x – 1)
-12x – C. 6(2x + 1)
-12x D. -6(2x + 1) C B
Answer: -5n D A

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

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

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

18. Factor the following: 2v+7v+14vB
7v( ) C
7v (1 + 2) D
v( )
Answer: D

19. 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

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