3/6/17 Name:___________________________
Simplifying Expressions through Distribution
Do Now: Chuck wants to paint a mural covering the entire two sections of the wall below. Write an expression that Chuck
could use to find exactly how much paint he needs to cover both and each sections of the wall.
__________________________
Ex 1) Write three expressions that are equivalent to 4(5 + 1)
1._________________________________________
2.______________________________________
3. ________________________________________
Ex 2) How can we rewrite 3(n + 2) using the distributive property?
Prove that they are equivalent! (Use substitution to demonstrate)
Key Point:
When there are parentheses in the expression, you must “DISTRIBUTE” whatever is on the outside of the parenthesis to
EVERYTHING on the inside of the parenthesis using _____________________________.
Quick Practice: Use the distributive property to write an equivalent expression.
1.) 5(4 + 6) =
2.) -3(6 – 2y) =
3.) y(2 – x) =
4.) 4(3x + 8)=
1
5.) 2 (20x + 10) =
Now, put it all together and simplify these expressions:
6. 2(3x + 4) + 8x + 6
7. -3(6 + 2x) + 12 + 3x
8. 4(x + 3) + 2x + 8
9. 3y + 8 + 4(6y + 3)
Independent Practice: Rewrite the expression using the distributive property.
1.) 6(15 + 12) = _________________
2
(6x
3
5(n + 2) = _____________
8(3 – p) = ___________
+ 12) = ____________________
2) For the following expression, rewrite using the distributive property. 12(y + 7) = ___________________ Would the
expressions be equivalent if the value for y was 3? Explain.
4.) Angel applied the distributive property and written an equivalent expression to 4(6 + 3). Did he do his work correctly?
Explain. 4(6 + 3) = 4(6) + 4(3)
__________________________________________________________________________________________________
__________________________________________________________________________________________________
During the summer, you make $80 per day plus whatever you make in commission, c. Write two equivalent expressions
to represent how much money you earn during a 5 day work week.
1: _______________________________
2: ________________________________
7.) Which expression below is equivalent to 48 + 3n?
a) 16(3 + n)
b) 3(16 + n)
c) 3(16 + 3n)
d) 48(1 + n)
8. 10(x – 5) + 5x – 6
9. -8(2x + 5) + 12x
10. -3(x – 8) + 5x + 20
Additional Practice:
A) Below is a swimming pool with a diving section. For the design, show two methods for calculating the total surface
area of the water.
B)Apply the distributive property to simplify the expression: 5(n + 2y – 3) 30
Simplifying Expressions with Distributive Property: Fluency Practice
Simplify each expression and find your answer on the accompanying picture. If time permits, color!
3/7/17 Name:____________________________
Partner(s):___________________________
1. 5x – 7(2 – 4x)
red
15. -2x + 7 – 3(-9 – 4x)
orange
2. 8 – 3(6 – 6x)
green
16. -1 + 5x – 9(-2 + 5x)
blue
3. 9x – 4(2x + 5)
blue
17. 9(3x – 9) – 7 – 2x
green
4. -3 – 8(-5x – 1)
brown
18. -4(5 + x) + x + 6
purple
5. -7x + 4(3x – 6)
purple
19. -6x – 2(-5x + 9) – 3x
blue
6. -8(2x – 4) + 5
brown
20. 5 – 8(1 – x) – 9x
blue
7. 2(x + 6) – 9x
orange
21. –x + 7 + 5(-4 + 7x)
yellow
8. -5(-7 – 3x) – 7
yellow
22. -6(-6x – 3) – 2 + 8x
orange
9. 4(-2x + 6) + x
purple
23. 4x – 5x + 3(x + 4)
orange
10. 4x – 9(3 – x)
blue
24. 7 + 9(-2n + 9) + 1
green
11. -8 – 8(6x + 1)
blue
25. −2𝑥 − 4 (12𝑥 − 8)
green
12. -5(-7 + x) – 7x
red
26. -5.4x + 4.2 – 1.6x + 3.8
purple
13. 4x – 7(3 – 3x) – 9
green
14. -8 + 6(-x – 3) + 4x
yellow
1
27.
1
𝑥
3
1
3
− 2 3 𝑥 + 2 (2 𝑥 − 6)
yellow
3/8/17 Factoring Linear Expressions
Activating Prior Knowledge: What is a factor?
Finding Factors – Examples
Directions: Find the greatest common factor (GCF) of the following:
1. 4, 12, 16
2. 12,18,9
3. 56, 16, 24
When we factor in math, we are finding the actual factors of the expression – that is, we are
looking for what was ________________, thus we are “un-_______________________.”
Factor:
1. 2𝑥 + 4 = ____(___𝑥 + ______)
2. −4𝑥 − 10 = ____(___𝑥 + ______)
3. 4𝑥 − 8
4. 16𝑥 + 22
5. A rectangle has an area of 4x + 6. If the width is 2, what is the length? (l x w)
6. A rectangle has an area of 9x – 12. If the width is 3x – 4, what is the length? (l x w)
Factor each expression. If the expression cannot be factored, write cannot be factored.
1. 15x + 10
2. 7x – 3
3. 6x + 9
4. 30x – 25
5. 13x + 14
6. 50x – 75
7. 24x – 18
8. 18x + 13
9. 16x – 12
10. 36x + 45
11. A square picture frame has a perimeter of (20x + 32) inches. What is the length of one
side of the picture frame? (Square perimeter = 4 x side)
12. The rectangle shown below has a total area of (4x + 36) square feet. Factor 4x + 36.
4x
36
3/9/17 Name:_______________________________
Algebraic Expressions Review
Write a numerical or algebraic expression for the following:
1. The difference between ten and four = ___________________________________
2. Five times a number= __________________________
3. The sum of 15 and a number= _________________________
Evaluate the following expressions: when x = 5
4. 3x - 8 = ___________
5. n2 – 4n - 5 = ___________
6. 2n2 - 10 =_____________
Write an expression for the following scenarios:
7. James ran a certain number of miles, m. Miranda ran 3 times the sum of m and 6. Write an expression to show how
many miles Miranda ran.
______________________________
8.
Combine like terms(distribute where needed):
9. 5x2 + 3y -x2 + 5 - 2y
10. -3 - 9x + 4 + 8x
11. 10 - 3(2x - 5) + 10x
12. 4(x - 3) - 2x + 6
Factor the following Expressions:
13. 6x + 15
14. 4x - 16
Write your own scenario for the expression:
7.99s + 2.25
15. 3x + 7
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Day
Homework
Monday (3/6)
Handout IP: #1-4, 7, 10
Tuesday (3/7)
Simplify Expression w/ Distribution- Complete 5 additional expressions
Wednesday (3/8)
Handout IP: #2-10 even
Thursday (3/9)
Quiz- Algebraic Expression