What are similar monomials?

Definition of similar monomials:

Similar monomials are monomials that can only differ in their coefficients and their literal parts are the same.

Examples will help you to understand what similar monomials are.

Example 1.

Is the monomial 2a similar to the monomial 5a?

Solution.

These two monomials differ in their coefficients (2 and 5) and not in their literal parts. It means that these two monomials are similar.

The answer: 2a is similar to 5a.

Example 2.

Is the monomial 23a^{3} similar to the monomial 56a^{3}?

Solution.

These two monomials differ in their coefficients (23 and 56) and not in their literal parts (a^{3}). It means that these two monomials are similar.

The answer: 23a^{3} similar to the 56a^{3}.

Example 3.

What monomial is similar to 3x?

Solution.

We know that similar monomials can only differ in their coefficients and not in their literal parts.

The monomial 4x is similar to 3x.

These two monomials differ in their coefficients (3 and 4) and not in their literal parts. It means that these two monomials are similar.

The answer: 4x is similar to 3x. There are many monomials similar to 3x: 150x, 3.56x,...

Example 4.

Is the monomial 4a^{5}b^{3}c^{2} similar to the monomial 33a^{4}b^{2}cabc?

Solution.

33a^{4}b^{2}cabc =

33a^{4 + 1}b^{2 + 1}c^{1 + 1} =

33a^{5}b^{3}c^{2}

33a

33a

These two monomials differ in their coefficients (4 and 33) and not in their literal parts. It means that these two monomials are similar.

The answer: 4a^{5}b^{3}c^{2} is similar to 33a^{4}b^{2}cabc.

See Similar monomials worksheet.