Identifying Like Terms

When we look at algebraic terms to find like terms, first we ignore the coefficients and only look if terms have the same variable(s) with same exponents. Those terms which qualify this condition are called like terms.

For example − Consider the terms, 2a, 5a, 9a, 13a

All the given four terms are like terms, because each of them have the same single variable ‘a’. These terms are having different coefficients but the same variable.

• The following are like terms as each term consists of a single variable, x, and a numeric coefficient.

  7x, 41x, 3x, 0x, -22x, -x

• Each of the following are like terms because they are all constants.

  18, -5, 27, 905, 0.8

• Each of the following are like terms because they are all y² with a coefficient.

  5y², 3y², -y², 29y²

For comparison, below are a few examples of unlike terms.

• The following two terms both have a single variable, but the terms are not alike since different variables are used.

  13x, 13y

• Each y variable in the terms below has a different exponent, therefore these are unlike terms.

  11y, 18y², 32y⁵

Identify the like terms in the following expression

5x + 7xy −7x + 11xy

Solution

Step 1:

Like terms consist of same variables raised to same exponents.

There are two pairs of like terms in this expression.

Step 2:

They are as follows.

5x and −7x; 7xy and 11xy;

5x and −7x have the same variable x

while 7xy and 11xy have the same combination of variables xy.

Identify the like terms in the following expression:

15m + 2n – 4m + n +12m

Solution

Step 1:

Like terms consist of same variables raised to same exponents.

Step 2:

The following are like terms because each term consists of variable, m, and a numeric coefficient.

15m, −4m, 12m

Step 3:

The following are like terms because each term consists of variable, n, and a numeric coefficient.

n, 2n