Method

Combining Like Terms

In an expression, groups of like terms can be combined to write an equivalent expression with the least possible number of terms. As an example, consider the following expression.

7 x y + 2 x - 3 x y - 2 x^{2} + x + 5 x^{2}

There are three steps to follow to combine like terms.

1

Identify Like Terms

Start by identifying the like terms in the expression. These are terms with the same variables raised to the same power. Also, all constants are like terms.

This expression has two

x -

terms, two

x y -

terms, and two

x^{2} -

terms.

2

Grouping Like Terms

Now that the like terms are identified, use the Commutative Property of Addition to rearrange the expression so that the like terms are grouped together.

3

Add and Subtract the Coefficients

Finally, combine the like terms by adding or subtracting the coefficients of the variables as well as adding or subtracting the constants.

Now that all like terms have been combined, the initial expression has been reduced to its simplest form.

7 x y + 2 x - 3 x y - 2 x^{2} + x + 5 x^{2} ⇕ 4 x y + 3 x + 3 x^{2}