Luttrell 2012
22
Name: ______________________
Date: _____
2f - Like Terms
Constant
: A number that doesn’t change. In the expression 2x + 3, the constant is 3. The 2 is a
coefficient
.
Variable
: A number that may change, usually is represented by a letter. In the expression 2x + 3, the variable is x.
Term
: Any constant or variable that is being added or subtracted. In the expression 2
x
+ 3
y
, the terms are 2
x
and 3
y
.
Expression
: A collection of terms that together represents a number.
Equation
: When two expressions are equal. Usually the goal is to find the value of the variable that makes the
equation true (equal).
Like Terms
: Two or more terms having the same variables with the same exponents. The variables do not need to
be in the same order; 2
wz
and 3
zw
are like terms. Coefficients are ignored since they refer to the amount of this
term you have.
Combining like terms
: When the terms are alike, you add or subtract (depends on signs) the coefficients. Adding
2
wz
and 3
zw
would give you 5
wz
. Subtracting 2
wz
from 3
zw
would result in 1
wz
(better written as
wz
).
1. Write a like term for each of the following:
a. -16
y
b. -5
c. 4
xy
2
z
d. 5
h
2. Determine which of the following sets are made up of like terms:
a. {4
x
, 3
x
2
, 3
x
3
}
b. {
xyz
, -3
xyz
, 5
yz
}
c. {2
xy
, -3
xy
, -8
xy
}
For the following exercises, combine like terms.
3. 5
x
2
- 6
x
2
+ 4
xy
+ 3
y
2
- 2
y
2
4. (8
y
2
+ 6
y
- ½) + (-
y
2
- 2
y
+ ¾)
5. (3
x
2
+ 4
x
+ 4) + (
x
2
- 2
x
- 2)
6. Add
x
2
- ¼ and -
x
2
- 5
x
+
⅞.
7. (5
x
3
- 10
x
2
+ 3
x
) - (-3
x
3
+ 5
x
2
- 8
x
0
)
8. (5
x
-3) - (- 4
x
2
+ 3
x
- 1)
9. Subtract -3
x
3
- 2
x
2
- 6
x
0
from -2
x
3
- 3
x
2
- 6
x
.
10.
(2 - x) - (4 + 5x)
11. Subtract 2
x
3
- 3
x
2
+ 4
x
from -2
x
3
- 3
x
2
+ 5
x
+4
x
0
.
12.
(3 + 3x) + (1 - 2x)