How to Subtract Monomials?

Monomials can be defined as that algebraic expression which is comprised of only one term such as ax p y q where ‘a’ is coefficient and 'x' and 'y' are representing the variables. Those terms are called like terms in which only coefficient changes. For instance, 5x and -7x, -4p and 9p, -3y² and -y² etc. are like terms. If there is a change in variable terms then they are said unlike terms. For instance, 6x and -4y, 2ab, 3cd, 8x and -9x² etc. are examples of unlike terms. Addition and subtraction is possible only in case when variables are similar or terms are like. For instance we can add or subtract ax p y q and b x p y q. Terms ax p and a xp yq  can neither be added nor subtracted. Addition and subtraction of monomials is also called as combining monomials.

Let’s see how to subtract monomials.
1)       First of all, be sure that two monomials to be subtracted are like terms (variable and exponent must be same). For instance, 4x² and -4x² are like terms, since they both have the same variable and exponents.

2)      Then take common variable terms and,

3)      Subtract the coefficients and write the resulting coefficient to left of the variable and exponent.

4)      After subtraction, sign of larger number will be used with the result.

Let’s take an example to understand subtraction:
Consider 9x² and 12x²?
Subtraction will be performed by taking common variable 'x' and exponent 2. This will be given as
9x² – 12x² = (9 – 12) x²,
Since sign of the term 12 is negative that’s why there will be negative result. And answer will be
9x² – 12x² = – 3x²,
Addition will be:
9x² + 12x² = (9 + 12) x² = 21x².