definition Terms are the parts of an expression that are being added and/or subtracted.
terms
This expression, 2x + 5, has two terms (2x and 5).
One term (2x) contains a variable, x.
The other term (5) is a number, referred to as a constant.

 

definition Like terms (or similar terms) are terms that represent the same quantities.
In algebra, these terms have the exact same variable part.
Consider the statement: Two cats plus three more cats equals a total of five cats.
cats
If we represent "cats" by the letter (variable) "c", we have, 2c + 3c = 5c.
In all three terms, "c" represents the same thing (the species "cat"),
so, the "c's" are referred to as
"like" terms.
Since the "c's" are like terms, their quantities can be added together.
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Terms that are not "like terms" cannot be added together.
Two cats and three dogs cannot be added together.
catsdogs
2c + 3d = 2c + 3d
Cats (c) and dogs (d) are not "like" terms, and cannot be added.

Like terms, are terms whose variables (including any exponents) are the same.
They are terms that look like each other.
The only difference will be the coefficients (the numbers in front of the variables).

Like Terms:
Notes:
3, 12, -4, 5x0
The simplest "like terms" are numbers (constants).
Remember that the "variable" in a constant term has an exponent of 0, making the variable equal to 1.
3x2 , 6x2 , -2x2 , x2
These are "like terms" because each has the variable factor of x2 .
4a2b3, a2b3, -3a2b3
These are "like terms" because each has the variable factor of a2b3.
Not Like Terms:
Notes:
3, 4xy, -2a, 5x2y
These terms do not have the same variable factor. Remember that xy and x2y are different terms. These examples are unlike terms.

Like terms can be combined under addition or subtraction.
This process is the same as adding apples to apples, and oranges to oranges.
Just remember to add only the terms that are "like".

Problem:
Answer:
• Simplify: 2x + 4x + x
Don't forget the implied "1" in front of x.
Think of it as two x's plus four more x's plus one more x.
You can also factor: x(2 + 4 + 1) = 7x
Answer: 7x
• Simplify: 2x2 + x - 5 + x2 - 4x + 9
Group the like terms together and them combine them. Remember when moving terms to move their signs with them. 2x2 + x2 + x - 4x - 5 + 9
Factor: x2 (2 + 1) + x (1 - 4) - 5 + 9
Answer: 3x2 - 3x + 4
• Simplify: 6x2 - (10 + 3x2 - 2x)
Deal with parentheses before you combine the like terms. In this case, distribute -1 across the parentheses. 6x2 -1(10 + 3x2 - 2x)
6x2 -10 - 3x2 + 2x =
6x2 - 3x2 + 2x -10
Answer: 3x2 + 2x -10
• Simplify: a2b + 2(3a2b - 5a)
Distribute the +2 across the parentheses.
a2b
+ 2(3a2b - 5a) = a2b + 6a2b - 10a
Answer: 7a2b - 10a
• Simplify: 5x2 - 4x3 - x2 + 8
Look carefully at the exponents.
Answer: - 4x3 + 4 x2 + 8


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Additional vocabulary associated with "terms":

If any, and all, exponents appearing in a term are whole numbers (0, 1, 2, 3, ...),
a term may be referred to as a
monomial.

Classification by Terms
monomial
one term:    12,    4x,    x2,    -5xy
binomial
two terms:    2x - 1,    x2 - 4
trinomial
three terms:    x2 + 2x + 1
polynomial - one or more terms
polynomial means "
many", but it can also be one term.
The ending of these words "nomial" is Greek for "part".
Classification by Degree
Linear - degree of 1 or 0:    3x + 1  or  12
Quadratic - degree of 2:   2x2 - x + 7
Cubic - degree of 3:   3x3 + 4x2 + 3x + 5
The degree of a term with whole number exponents is the sum of the exponents of the variables, if there are variables. Non-zero constants have degree 0, and the term zero has no degree.
Example: 6x2 has a degree of 2  
4x2y3 has a degree of 5
(the sum of 2 and 3)
The degree of a polynomial is the highest degree of its terms.
Example: 3x2 + 4x + 1 has a degree of 2
 x3 - x2 + 5x - 2 has a degree of 3

 

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