Like terms

In mathematics, like terms are summands in a sum that differ only by a numerical factor. Like terms can be regrouped by adding their coefficients. Typically, in a polynomial expression, like terms are those that contain the same variables to the same powers, possibly with different coefficients. More generally, when some variable are considered as parameters, like terms are defined similarly, but "numerical factors" must be replaced by "factors depending only on the parameters". For example, when considering a quadratic equation, one considers often the expression where and are the roots of the equation and may be considered as parameters. Then, expanding the above product and regrouping the like terms gives In this discussion, a "term" will refer to a string of numbers being multiplied or divided (that division is simply multiplication by a reciprocal) together. Terms are within the same expression and are combined by either addition or subtraction. For example, take the expression: There are two terms in this expression. Notice that the two terms have a common factor, that is, both terms have an . This means that the common factor variable can be factored out, resulting in If the expression in parentheses may be calculated, that is, if the variables in the expression in the parentheses are known numbers, then it is simpler to write the calculation . and juxtapose that new number with the remaining unknown number. Terms combined in an expression with a common, unknown factor (or multiple unknown factors) are called like terms. To provide an example for above, let and have numerical values, so that their sum may be calculated. For ease of calculation, let and . The original expression becomes which may be factored into or, equally, This demonstrates that The known values assigned to the unlike part of two or more terms are called coefficients. As this example shows, when like terms exist in an expression, they may be combined by adding or subtracting (whatever the expression indicates) the coefficients, and maintaining the common factor of both terms.