Like Terms
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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.
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.
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.
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
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.
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.
Constants as Like Terms:
- 6 and 9: Constants are also considered like terms because they have no variables.
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