Combine Like Terms
Combining like terms
Simplify expressions by combining like terms. At the bottom of this page you will find practice problems and a worksheet generator.

• What you need to know
• A term is
• A number by itself (called a constant or constant term), examples are:  3, -5, 17.
• A variable by itself (any term that has a variable is called a variable term),
examples are :  x, y, z.
• The product of numbers and variables or the product of just variables, examples are:  2x, -3xy, x2y3.
• The sign in front of the term is part of the term and must be included with the term.
If the term has a double operator in front of it you must replace the double operator with its equivalent single operator to get the correct sign for the term.
For example:
- -3x is + 3x or 3x.  The term is 3x and it is positive.
+ -4x is -4x.  The term is -4x and it is negative.
• Like terms
• Constant terms (numbers by themselves) are like terms, examples are:  7, -23, 0.
• Variable terms with the same variables and the same exponents on those variables.
These are all like terms:  2x3y2, -5x3y2, x3y2. Even though they don't have the same coefficients (number part) they are like terms because each term has the same variables (x and y) and those variables have the same exponents in each term (x3 and y2).
• Unlike terms
• 3x and 3y are unlike terms because they don't have the same variables.
• -5x2y3 and xy3 are unlike terms even though each term has the same variables because the exponent on the x variable is not the same for both terms. ( The exponent on the x in the -5x2y3 term is 2 while the exponent on the x in the term xy3 is a 1. When the exponent is not shown it is automatically a 1).
• To combine like terms
• Clear all double operators
• The sign in front of a term is part of the term
• Add the number parts of the like terms to get one new term with the same variables.
Example:  2xy + xy = 3xy
(when you don't see a number in front of a variable term it is automatically a 1 so xy is acutally 1xy)

Problem # 1