1. SWBAT… use the distributive property to simplify expressions
Tues, 8/28
Agenda
Warm-up (10 min)
CLT and Distributive property (30 min)
OYO (On Your Own) practice problems (10 min)
Warm-Up:
Evaluate the expressions when x = -3 and y = -5
1.) 2x2 – y + x 2.) x3 + y2 3.)
HW#2: Simplifying Algebraic Expressions
1.) 2x2 – y + x
2(-3)2 – (-5) + (-3)
2(9) (-3)
(-3) 20
2.) x3 + y2
(-3)3 + (-5)
3.) 4/5x – 2 2/5
4/5(-3) – 12/5
-12/5 – 12/5
-24/5
-4 4/5

2. Simplifying Algebraic Expressions by Combining Like Terms
Infinity HS
Ms. Sophia Papaefthimiou

3. Like Terms are terms with the same variable AND the same exponent.

4. Are these like terms? 1) 13x, 22x 2) 5ab, 4ba 3) 5x, 25
Yes, the variables and exponents are the same.
2) 5ab, 4ba
Yes, the order of the variables doesn’t matter.
(ab = ba. Commandment #9)
3) 5x, 25
No, the 25 does not have a variable x

5. 1.) Which of the following is the simplified form of -4x + 7x ?
Don’t forget the negative!

6. 2.) Which of the following is the simplified form of 5x – 4 – 7x + 14 ?

7. 3.) Which of the following is the simplified form of 5x – 4x2 – 7x + 14x2 ?

8. 3.) -4d – 6a2 +2d – 12a2
-18a2 – 2d
4.)
5.) y

9. Simplifying Algebraic Expressions using the Distributive Property
Infinity HS
Ms. Sophia Papaefthimiou

10. The Distributive Property
The process of distributing by multiplying the number and/or variable on the outside of the parentheses to each term on the inside.
a(b + c)
a(b + c) = ab + ac
a(b – c)
a(b – c) = ab – ac
Example #1
5(x + 7)
(5)(x) + (5)(7)
5x + 35

11. 3(m – 4) (3)(m) – (3)(4) 3m – 12 -2(y + 3) (-2)(y) + (-2)(3)
Example #2
3(m – 4)
(3)(m) – (3)(4)
3m – 12
Example #3
-2(y + 3)
(-2)(y) + (-2)(3)
-2y + (-6)
-2y – 6

12. -5(z – 9) (-5)(z) – (-5)(9) -5z + 45 -(n2 + n – 25)
Example #4
-5(z – 9)
(-5)(z) – (-5)(9)
-5z + 45
Example #5
-(n2 + n – 25)
(-1)(n2) + (-1)(n) – (-1)(25)
-n2 – n + 25

13. Which statement demonstrates the distributive property incorrectly?
3(x + y + z) = 3x + 3y + 3z
(a + b)c = ac + bc
5(2 + 3x) = x
6(3k – 4) = 18k – 24
Answer Now

14. p = 10t – 100 p = -10t p = 7t – 15 p = 10t – 20 Answer Now
The algebraic rule p = 5(2t – 20) expresses the profit, p, for a school dance in terms of the number tickets sold, t. Which is an equivalent form of this rule?
p = 10t – 100
p = -10t
p = 7t – 15
p = 10t – 20
Answer Now

15. Let’s put distributive property and CLT together!
5(z – 3) + 4z (HW#2, Prob #9)
5z – z
9z – 15
4(y2 + 8y – 2) – y2 + y
4y2 + 32y – 8 – y2 + y
3y2 + 33y – 8
5(3x – 7) – 6x (HW#2, Prob #12)
15x – 35 – 6x
9x – 35

16. Simplify each expression
1) 5a2 + 7a
Simplified
2) -4x2y + x2y – x2y + x2
-4x2y + x2
3) a + 3a – 4(9 – a)
8a – 36
4) If a triangle has sides 3x – 2, 5 – x and 2x – 5, what is the perimeter of the triangle?
4x – 2

17. SWBAT… simplify algebraic expressions
Wed, 8/29
Agenda
Warm-up (15 min)
Review HW#1 & 2 (35 min)
Warm-Up: Simplify:
-3x(x3 – 2x2)
7(4x2 + 3x) – 2(5x2 + x)
6x + 4[7 – (x – 2)] (First distribute -1)
Back of agenda problems: Quiz tomorrow
1. 3x4 + 6x3
28x2 + 21x – 10x2 – 2x (now CLT)
18x2 + 19x (HW#2, Problem #15) 17

18. Simplify -x2 – 3xy + 4y3 for x = -3 and y = -1
Practice Problems:
Simplify for x = -2 and y = 4
Simplify -x2 – 3xy + 4y3 for x = -3 and y = -1
Simplify 10y2 – 1 for y = √8 (square root of 8)
-22 79 18

19. SWBAT… simplify algebraic expressions
Fri, 8/31
Agenda
WU (5 min)
Quiz (30 min)
Two-step equations
Warm-Up: Simplify:
Evaluate -x2 – 3xy + 4y2 for x = -3, y = -1
Simplify -x2 – 3x + 4x2 – x2 + 10x
-14
2x2 + 7x 19