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LESSON 7.2 Day 2
The Distributive Property
Goal: Use the distributive property.
EXAMPLE 1 - Finding a Combined Area – Distributing Numbers
Gardening: You are planting a vegetable garden and a flower garden. The diagram shows the
dimensions of the two adjacent, rectangular gardens. How can you find the total area of the two
gardens?
Method 1 Find the area of each garden, then find the total area.
Area =
=
+
=
square feet
Method 2 Find the total length, then multiply by the common width.
Area =
=
=
(
(
)
)
square feet
The Distributive Property
Algebra a(b + c) = ab + ac
a(b – c) = ab – ac
Numbers 9(4 + 6)
8(x – 1)
EXAMPLE 2 - Using the Distributive Property – One Way to Simplify an Expression
Since you can’t add what is inside of the parenthesis, you must distribute the number outside of the
parenthesis to both terms inside of the parenthesis.
a) 4(a + 3)
b) (a + 5) 6
c) 3(x – 8)
d) 9(2p + 7)
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EXAMPLE 3 - Distribute a negative number
a) –3 (7 + 3x)
b) (6  a)( 2)
c) -7(-x – 3)
d) -(x – 4)
1)
Now You try it. Use the distributive property to write an equivalent expression.
5 (n + 4)
2)
 (3 + 4a)
3)
–3(2x – 7)
4)
-9(-x + 4)
EXAMPLE 4 - Simplifying an Expression – Putting it All Together:
1) Always distribute first!
2) Then combine like terms.
a. 2(9 + n) + 3n
b. –7(3y – 1) + y – 2
c.
4x – 2 (x – 4)
Now You Try It! Simplify the expression.
5)
6(m – 7) – m + 12
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