How to add monomials with exponents? How to add monomials with exponents of one?

Example of adding monomials with exponents.

Add the following monomials with exponents

15a^{5} + 5a^{5}

Solution.

15a^{5} + 5a^{5} =

20a^{5}

20a

The answer 20a^{5}.

Example of adding monomials with exponents.

Add the following monomials with exponents

2a^{3} + a^{3}

Solution.

2a^{3} + a^{3} =

2a^{3} + 1 * a^{3} = 3a^{3}

2a

The answer 3a^{3}.

Example of adding monomials with exponents.

Add the following monomials with exponents

8a + 7a

Solution.

Where are the exponents here? The exponent is equal to one.

8a + 7a =

8a^{1} + 7a^{1} =

15a^{1} = 15a

8a

15a

The answer 15a.

Example of adding monomials with exponents.

Add the following monomials with exponents

12a^{4} + 10a^{4} + 8a^{3}

Solution.

Here 12a^{4} and 10a^{4} are like terms (monomials). We can add them

12a^{4} + 10a^{4} = 22a^{4}

The 22a^{4} and 8a^{3} are unlike terms (monomials). We cannot add them.

The answer 22a^{4} + 8a^{3}.

See the definition of unlike terms.