A term is a single mathematical expression.
It may be a single number (positive or negative), a single variable ( a letter ), several variables
multiplied but never added or subtracted. Some terms contain variables with a number in front
of them. The number in front of a term is called a coefficient.
Examples of single terms:
3x is a single term. The "3" is a coefficient. The "x" is the variable.
-5x2
y
3
z
4 is also a single term.
The "-5" is the coefficient. " x
2
y
3
z
4
" are the variables comprising the term.
12 is a single term.
It is simply a numerical term called a constant.
w is a single term too.
It is a single variable term and since there is only one "w" it has an implied coefficient of 1 .
We join terms together with addition to create expressions.
5x + 7y is a two termed expression.
The 5x is one term and the 7y is the second term. The two terms are separated by a plus sign.
7x2
y
3
- 2xy
4
+ 7 is a three termed expression.
7x2
y
3
is one term, - 2xy
4
is the second term, and 7 is the third term.
The coefficient of the first term is 7.
The coefficient of the second term is negative 2.
The third term is a constant, so it has no coefficient.
Like Terms
"Like terms" are terms which have variables which look EXACTLY alike.
3x2
and -7x2
are "like terms" because both terms have the variable x
2
5x2
y
6
z
5
, 13x2
y
6
z
5
, and -21x2
y
6
z
5
are "like terms" because all of the terms have the variables "
x
2
y
6
z
5
" in them.
Combining Like Terms
To combine "like terms", combine the coefficients of terms which look exactly alike.
If you start with several terms separated by addition and subtraction signs, your answer should
also contain addition and subtraction signs based on the signs obtained from doing the
arithmetic.
Combine like terms:
3x2
+ 2x + 9 - 2x
2
+ 5x - 3
3x2
+ 2x - 9 - 2x
2
+ 5x - 3
(3 - 2 )x
2
+ (2 + 5 )x + (-9 - 3 )
1x2
+ 7x + (-12)
1x2
+ 7x - 12
You may be required to perform some other algebraic operations before you are ready to
combine like terms.
Simplify. Combine like terms:
-5( 2x3
- 3x2
+ 1) + 2(-2x
3
+ 5x2
- 1)
Distribute the -5 into the first parentheses and multiply.
Do the same with the 2 in front of the second parentheses.
-5(2x
3
) -5(-3x
2
) -5(1) + 2(-2x
3
) + 2(5x2
) + 2(-1)
-10x
3
+ 15x
2
-5 -4x3
+10x2
-2
Now combine like terms,
(-10 - 4 )x
3
+ (15 + 10)x
2
+ (-5 - 2)
-14x3
+25x2
-7
Step-by-step explanation:
