1. The Distributive Property
Objective: I will use the distributive
property to simplify expressions and equations.

2. The Distributive Property
The process of distributing the number on the outside of the parentheses to each term on the inside.
a(b + c) = ab + ac and (b + c) a = ba + ca
a(b - c) = ab - ac and (b - c) a = ba - ca
Example #1
5(x + 7)
5 • x + 5 • 7
5x + 35

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

4. 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

5. A term is a 1) number, 2) variable, or
3) a product / quotient of numbers and variables.
Example 5 m
2x2

6. the numerical part of the term.
The coefficient is
the numerical part of the term.
Examples
1) 4a 4
2) y2 1 3)

7. Like Terms are terms with the same variable AND exponent.
To simplify expressions with like terms, simply combine the like terms.

8. Are these like terms? 1) 13k, 22k Yes, the variables are the same.
2) 5ab, 4ba
Yes, the order of the variables doesn’t matter.
3) x3y, xy3
No, the exponents are on different variables.

9. Which of the following is the simplified form of -4x + 7x ?
Answer Now

10. 5a and a are like terms
and
are like terms
The above expression simplifies to:

11. Simplify 1) 5a + 7a 12a 2) 6.1y - 3.2y 2.9y 3) 4x2y + x2y 5x2y
4) 3m2n + 10mn2 + 7m2n - 4mn2
10m2n + 6mn2

12. 5) 13a + 8a + 6b
21a + 6b
6) 4d + 6a2 - d + 12a2
18a2 + 3d 7) y

13. Which of the following is the simplified form of 5x - 4 - 7x + 14 ?
Answer Now

14. If a triangle has sides 3x - 2, 5 - x and 2x - 5, what is the perimeter of the triangle?
Answer Now

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

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

17. Opposite of an expression
-(4a – 3b + 7c)
Change everything on the inside to its opposite
-4a + 3b – 7c

18. Simplifying using the distributive property
5x – 9 + 3(2x + 4)
5x – 9 + (3)(2x) + 3(4)
5x – 9 + 6x + 12
5x + 6x = 11x
= 3
Answer: 11x + 3

19. Distributive Property
Taking the opposite can be considered distributing -1
(4a – 3b + 7c) = -1(4a – 3b + 7c)

20. Distributing a negative
-4(y + 2) = (-4)(y) + (-4)(2)
= -4y + (-8)
= -4y – 8

21. Using the Distributive Property to Simplify
9t – 5r – 2(3r + 6t)
9t – 5r – 6r – 12t
9t – 12t = -3t
-5r – 6r = -11r
Answer: -11r – 3t