Like Terms

Diagram depicting the algebraic expression 5x + 3, with arrows pointing to each component labeled 'Coefficient' for the 5, 'Variable' for the x, and 'Constant' for the 3.
Dissecting the algebraic expression 5x + 3 to identify and understand like terms, which are terms in an algebraic expression that have the same variable raised to the same power.

Table of Contents

Algebra Like Terms

Like terms are algebraic terms that share the same variables and the same exponents on those variables. They can be combined using the basic rules of arithmetic because they represent similar mathematical quantities.

  1. Same Variable(s): Like terms have identical variables, meaning they are the same letters or symbols. For example, 3x and 7x are like terms because they both have the variable x.

  2. Same Exponent(s): The variables in like terms have the same exponents. For example, 2y^2 and 5y^2 are like terms because they both have the variable y raised to the power of 2.

  3. Coefficients: Like terms can have different coefficients, which are the numerical factors multiplying the variables. For example, 4a and \text{-}2a are like terms because they share the variable a.

Examples of Like Terms

  1. Like Terms with Variables:

    • 3x and 7x: These are like terms because they have the same variable x.
    • 2y^2 and 5y^2: These are like terms because they have the same variable y raised to the power of 2.
  2. Like Terms with Different Coefficients:

    • 4a and \text{-}2a: These are like terms because they share the same variable a, even though the coefficients are different.
  3. Constants as Like Terms:

    • 6 and 9: Constants are also considered like terms because they have no variables.
  4. Combining Like Terms:

    • 2x+3x-5x: The terms 2x, 3x, and \text{-}5x are like terms because they share the same variable x. Combining them yields 2x+3x-5x=0.

Related Links

Coefficient

Factors

Monomial

Polynomial