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```Ch01pgs053-065
1/19/06
7:38 AM
Calculate.
23. a) 45 3
b) 4 5 4 3
Page 58
In the statement of the distributive law, we know that in an expression
such as ab ac, the multiplications are to be done first according to the rules
for order of operations. So, instead of writing 4 5 4 7, we can write
4 5 4 7. However, in ab c, we cannot omit the parentheses. If we did,
we would have ab c, which means ab c. For example, 34 2 18,
but 3 4 2 14.
There is another distributive law that relates multiplication and subtraction. This law says that to multiply by a difference, we can either subtract and
then multiply, or multiply and then subtract.
24. a) 2 5 3
THE DISTRIBUTIVE LAW OF
MULTIPLICATION OVER SUBTRACTION
For any numbers a, b, and c,
ab c ab ac.
b) 2 5 2 3
25. a) 5 2 7
We often refer to “the distributive law” when we mean either or both of
these laws.
Do Exercises 23–25.
b) 5 2 5 7
What do we mean by the terms of an expression? Terms are separated by
addition signs. If there are subtraction signs, we can find an equivalent expression that uses addition signs.
EXAMPLE 13
We have
What are the terms of the
expression?
26. 5x 8y 3
What are the terms of 3x 4y 2z?
3x 4y 2z 3x 4y 2z.
Separating parts with signs
The terms are 3x, 4y, and 2z.
Do Exercises 26 and 27.
27. 4y 2x 3z
The distributive laws are a basis for a procedure in algebra called multiplying. In an expression like 8a 2b 7, we multiply each term inside the
parentheses by 8:
Multiply.
8a 2b 7 8 a 8 2b 8 7 8a 16b 56.
28. 3x 5
EXAMPLES
29. 5x 1
Multiply.
14. 9x 5 9x 95
Using the distributive law of multiplication
over subtraction
9x 45
30.
2
3 w
1 23 w 23 w 2
3
1
Using the distributive law of multiplication
2
3
16. 43 s t w 43 s 43 t 43 w
Using both distributive laws
Do Exercises 28–30.
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CHAPTER 1: Introduction to Real Numbers
and Algebraic Expressions