What are the steps and rules for adding and subtracting monomials?

Answer 1

A monomial is a polynomial that has just one term. So to add or subtract monomials, is the same as we add or subtract like terms (terms that have exactly the same variable part). Since we are dealing with monomials, the restriction is that the exponent(s) of the variable(s) must be positive integer(s).

Examples of monomials:

10xy, -5xy2, -3x2, 3w3z6, -7xy, -4x2, 2xy2, 9w3z6.

So, how to add or subtract them?

First detect where the like terms (monomials) are,

then group them (write them next to each other),

then combine (ad or subtract their coefficients, and write next to the result the common variable part).

10xy -7xy = 3xy (subtract since the coefficients have different sign).

-5xy2 +2xy2 = -3xy2 (subtract since the coefficients have different sign).

-3x2 -4x2 = -7x2 (add because the coefficients have the same sign).

3w3z6 + 9w3z6 = 12w3z6 (add because the coefficients have the same sign).