How to add monomials with different exponents? How do you add monomials with different exponents?

Example of adding monomials with different exponents.

Add the following monomials with different exponents

4a^{5} + 4a^{4}a

Solution.

4a^{5} + 4a^{4}a =

4a^{5} + 4a^{4}a^{1} =

4a^{5} + 4a^{4 + 1} =

4a^{5} + 4a^{5} = 8a^{5}

4a

4a

4a

Answer: 8a^{5}.

Example of adding monomials with different exponents.

Add the following monomials with different exponents

5a^{2}b + 4aab

Solution.

5a^{2}b + 4aab =

5a^{2}b + 4a^{1}a^{1}b =

5a^{2}b + 4a^{1 + 1}b =

5a^{2}b + 4a^{2}b = 9a^{2}b

5a

5a

5a

Answer: 9a^{2}b.

Example of adding monomials with different exponents.

Add the following monomials with different exponents

6bb + b^{2}

Solution.

6bb + b^{2} =

6b^{1}b^{1} + b^{2} =

6b^{1 + 1} + b^{2} =

6b^{2} + 1 * b^{2} = 7b^{2}

6b

6b

6b

Answer: 7b^{2}.

Example of adding monomials with different exponents.

Add the following monomials with different exponents

14x^{3} + x^{3} + x^{2}

Solution.

14x^{3} + x^{3} + x^{2} =

(14x^{3} + x^{3}) + x^{2} =

15x^{3} + x^{2}

(14x

15x

Answer: 15x^{3} + x^{2}.

Note, we can only add like terms (monomials) and we cannot add unlike terms (monomials).

See the adding unlike monomials.

See the adding like monomials.