## Monomials

A **monomial** is an algebraic expression that consists of only one term. (A *term* is a numerical or literal expression with its own sign.) For instance, 9x , -4a², and 3mpx³ are all monomials. The number in front of the variable is called the numerical **coefficient**. In -9*xy*, -9 is the coefficient.

### Adding and subtracting monomials

To *add* or *subtract monomials,* follow the same rules as with signed numbers, * provided that the terms are like.* Like terms have the same pronumeral part, i.e. the same letters. E.g., and , but and are not like. Notice that you add or subtract the coefficients only, and leave the variables as they are.

**For example**

When terms or monomials contain the same variable and same exponent, they are like terms. Addition of monomials is done by adding the coefficients, without changing the variables nor the exponents.

3 *x* + 2 *x* = (3+2)x = 5 *x*

8y + 3y = (8 + 3)y = 11y

4np^{3} + 8np^{3} = (4 + 8)np^{3 }= 12 np^{3}

7 + 7x + 13x = 7 + (7 + 13)x = 20x + 7

**For example**

To subtract monomials, follow the same rules as with numbers, __provided that the terms are like__.

Let us subtract 12x from 10x

Given monomials are, 12x and 10x

12x-10x = (12-10)x = 2x

Remember

The letters and exponents never change; only the numbers out front change.

Whatever letters are in the problem are the same in the answer.

**YOU CANNOT ADD NOR SUBTRACT TERMS THAT ARE NOT LIKE!!**