Examine the polynomial 5x + 4. There are two terms, 5x and 4. The first term contains a variable, x, and a coefficient, 5. The term 4 is called a constant because it does not change. This polynomial has one variable.
Examine the expression 5x + 2y. This binomial has two variables, x and y.
Examine the expression 4x + 6x + 5y. This trinomial has two variables, x and y, but in this case, x appears twice. Because the variables have the same power, they are like terms. Combine the like terms by adding the coefficients before the variable, 4 + 6 = 10, and attaching the variable, 10x. The simplified binomial 10x + 5y remains, still with two variables. You can also combine terms by subtracting if the expression indicates subtraction.
Examine the expression 9x^3 -12x^2 + 15x. In this case, there is one variable, x. However, each x has a different power, which changes the value of the variable. Therefore, you cannot combine them but must count them individually as three variables: x cubed, x squared and x.
Examine the expression 4ab + 6a + 3b + 8ab + 24c. This expression has four variables: a, b, ab and c. Remember to combine any like terms. In this case, they form the variable set ab. 12ab + 6a + 3b + 24c. You cannot combine the separate terms a and b because the value of a + b does not equal the value of a x b.