Sum of monomials

A single-term algebraic expression is called a monomial. A monomial is the product of real numbers and variables with nonnegative exponents.

How to recognize a monomial?

Examples: -2abc; 3/x; -r^2s; 3/4x; xy^-3

-2abc and -r^2s are monomials

3/x, 3/4x, and xy^-3 are not monomials because each has an unknown variable in the denominator (xy^-3 = x/y^3).

The number in front of the variable, or numerical factor, is called the numerical coefficient of the term, or simply coefficient.

Examples:

2x^2, the coefficient is 2;

x^5, the coefficient is 1;

-3y, the coefficient is -3;

-6a/7, the coefficient is -6/7.

Terms that have the same variable factors are like terms. Monomials with the same like terms can be combined. For example,

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

5x^2y^3 - 2x^2y^3 = (5 - 2)x^2y^3 = 3x^2y^3

But 8xy and x cannot be combined because one monomial has x and y as its variables and the second monomial has only x. Therefore, the monomials are not like terms, and the resulting expression will remain 8xy +y.