Download A1EN0107 - MathChamber

Class
Name
1-7
Date
Enrichment
The Distributive Property
The Distributive Property can be used more than once in the same expression. In
this lesson, you learned that basic multiplication calculations can be completed
using mental math.
3 · 84 = 3(80 + 4) = 3(80) + 3(4) = 240 + 12 = 252
The same process can be used when both numbers are two-digit numbers. However, the
Distributive Property must be used more than once. Look at the following example.
(49)(26) = (40 + 9)(20 + 6)
Rewrite 49 as 40 + 9 and 26 as 20 + 6.
= (40)(20 + 6) + (9)(20 + 6)
(20 + 6) can be distributed into (40 + 9).
= (40)(20) + (40)(6) + (9)(20) + (9)(6)
Distribute 40 and 9 into (20 + 6).
= 800 + 240 + 180 + 54
Multiply.
= 1274
Add.
Exercises
Use the Distributive Property to find each product. Show your work.
1. (15)(32)
2. (48)(72)
3. (84)(63)
This same procedure can be utilized for simplifying algebraic expressions. Instead of
(20 + 2)(30 + 1), the expression might be (x + 2)(x + 1).
(x + 2)(x + 1)
= (x)(x + 1) + (2)(x + 1)
(x + 2) can be distributed into (x + 1).
= (x)(x) + (x)(1) + (2)(x) + (2)(1)
Distribute x and 2 into (x + 1).
= x2 +x + 2x +2
= x2 + 3x + 2
Multiply.
Add.
Exercises
Use the Distributive Property to find each product. Show your work.
4. (x + 3)(x + 4)
5. (x + 1)(x + 8)
6. (x + 4)(x + 2)
7. (x + 1)2 (Hint: Remember that (x + 1)2 = (x + 1)(x + 1).)
Prentice Hall Algebra 1 • Teaching Resources
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