Final answer:
To combine like terms in algebra, variables and their exponents must match; coefficients can vary. Terms are combined by adding or subtracting these coefficients.
Step-by-step explanation:
In order to combine like terms in an algebraic expression, the two things that MUST be the same are the variables and the exponents on those variables. The coefficients of the terms do not need to be the same; in fact, the process of combining like terms often involves adding or subtracting the coefficients of terms with the same variable and exponent. For example, in the expression 3x^2 + 4x^2, the like terms can be combined because they both contain the variable x raised to the same power, which is 2, resulting in 7x^2.
When dealing with standard mathematical functions or conversion factors involving equations, it is essential for terms to have the same dimensions to make sense of the operations. This rule ensures that we only add or subtract quantities that are compatible, similar to preventing the nonsensical addition of apples and oranges.
In order to combine like terms, variables and coefficients must be the same. Like terms are terms that have the same variables with the same exponents and the same coefficients. For example, 2x and 3x are like terms because they have the same variable, x, with the same coefficient, 2 and 3 respectively.