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

(

x

−

r

)

(

x

−

s

)

,

{\displaystyle (x-r)(x-s),}

where

r

{\displaystyle r}

and

s

{\displaystyle s}

are the roots of the equation and may be considered as parameters. Then, expanding the above product and regrouping the like terms gives

x

2

−

(

r

+

s

)

x

+

r

s

.

{\displaystyle x^{2}-(r+s)x+rs.}

Generalization

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:

a

x

+

b

x

{\displaystyle ax+bx}

There are two terms in this expression. Notice that the two terms have a common factor, that is, both terms have an

x

{\displaystyle x}

.