70 CHAPTER 1 The Real Number System
CAUTION It is important to be able to distinguish between termsand factors.
Consider the following expressions.
This expression has two terms, and.
Terms are separated by or symbol.This is a one-termexpression.
The factors and are multiplied.OBJECTIVE 3 Identify like terms. Terms with exactly the same variables that
have the same exponents are like terms.Here are some examples.
Like Terms Unlike Terms
and and Different variables
and and Different exponents
and and Different exponents
3 x^2 y and 5 x^2 y - 7 wz^3 and 2 xz^3 Different variables
- 2 pq 11 pq 4 xy^24 xy
6 x^2 - 5 x^217 x - 8 x^2
9 t 4 t 4 y 7 t
8 x^312 x^218 x^32112 x^22
a+ -8 x^312 x^28 x^3 + 12 x^2
NOW TRY
EXERCISE 1
Simplify each expression.
(a)
(b) - 4 - 1 - 3 y+ 52
312 x- 4 y 2(d)
Distributive property
Multiply.
Commutative property= 13 - 2 y Add. NOW TRY
= 5 + 8 - 2 y
= 5 - 2 y+ 8
= 5 - 112 y 2 - 11 - 82
= 5 - 112 y- 82 - a=- 1 #a
5 - 12 y- 82
NOTE The steps using the commutative and associative properties will not be shown
in the rest of the examples. However, be aware that they are usually involved.
OBJECTIVE 2 Identify terms and numerical coefficients.A termis a num-
ber, a variable, or a product or quotient of numbers and variables raised to powers,
such as
and k. Terms
In the term the numerical coefficient,or simply coefficient,of the variable x
is 9. Additional examples are shown in the table in the margin.
9 x,
2
p
9 x, 15 y^2 , -3, - 8 m^2 n, ,
NOW TRY ANSWERS
- (a) 6 x- 12 y (b) 3 y- 9
Numerical
Term Coefficient
88
7 y 7
34
26
1
11
3x
3 =1 x
3 =1
3 x38 x= (^38) x (^38)
r, or 1 r
- k, or - 1 k -
- 26 x^5 yz^4 -
34 r^3Be careful
with signs.(c)
Distributive property
Associative property
Multiply.
Commutative property= 21 + 12 k Add.
= 6 + 15 + 12 k
= 6 + 12 k+ 15
= 6 + 13 # 42 k+ 3152
= 6 + 314 k 2 + 3152
6 + 314 k+ 52
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