Distributive

1. Objective
The student will be able to:
use the distributive property to
simplify expressions.
Adapted from: Skip Tyler, Varina High School and Nicole Kessinger, Deep Run High School

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 - acand(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?
1.3(x + y + z) = 3x + 3y + 3z
2.(a + b) c = ac + bc
3.5(2 + 3x) = 10 + 3x
4.6(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
2x
2

6. The coefficient is
the numerical part of the term.
Examples
1) 4a
4
2) y
2
1
3)
5x
2
7
5
7

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) x
3
y, xy
3
No, the exponents are on different
variables.

9. Which of the following is the simplified
form of
-4x + 7x ?
1.-4
2.3x
3.-3x
4.4
Answer Now

10. 8x
2
+2x
2
+5a+a
The above expression simplifies to:
10x
2
+6a
8x
2
2x
2
5a and a are like terms
and are like terms

11. 12a
2) 6.1y - 3.2y
2.9y
3) 4x
2
y + x
2
y
5x
2
y
4) 3m
2
n + 10mn
2
+ 7m
2
n - 4mn
2
10m
2
n + 6mn
2
Simplify
1) 5a + 7a

12. 21a + 6b
6) 4d + 6a
2
- d + 12a
2
18a
2
+ 3d
3y
4
+
y
4
7)
3y
4
+
1y
4
=
4y
4
=1y
y
5) 13a + 8a + 6b

13. Which of the following is the simplified
form of
5x - 4 - 7x + 14 ?
Answer Now
1.-12x + 10
2.-2x + 10
3.2x - 18
4.12x – 18

14. If a triangle has sides 3x - 2, 5 - x and 2x - 5,
what is the perimeter of the triangle?
Answer Now
1.4x - 2
2.4x + 2
3.5x - 2
4.5x - 7

15. Which figure below models the simplification
of - 4x - 5 + 7x + 7 using these tiles?
Answer Now
1.
2.
3.
4.

16. Bonus! Which of the following is the
simplified form of a + 3a - 4(9 - a) ?
Answer Now
1.-36
2.3a - 36
3.8a - 36
4.8a + 36