Method

Combining Like Terms

Every group of like terms in an expression can be combined to write an equivalent expression with the least 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 of the expression. These terms are the terms with the same variables raised to the same coefficients. Also, all constants are like terms.

2

Grouping Like Terms

Then, rearrange the expression so that the like terms are grouped together. Remember that this is possible by the Commutative Property of Addition.

3

Add and Subtract the Coefficients

Finally, like terms can be combined 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,

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

has been reduced to its simplest form,

4 x y + 3 x + 3 x^{2} .