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

Example of adding and subtracting monomials with exponents.

Add and subtract the following monomials with exponents

81x^{5} + 4x^{5} - 3x^{5}

Solution.

81x^{5} + 4x^{5} - 3x^{5} =

82x^{5}

82x

The answer 82x^{5}.

Example of adding and subtracting monomials with exponents.

Add and subtract the following monomials with exponents

3x^{5} + 2x^{5} - x^{5}

Solution.

3x^{5} + 2x^{5} - x^{5} =

3x^{5} + 2x^{5} - 1x^{5} = 4x^{5}

3x

The answer 4x^{5}.

Example of adding and subtracting monomials with exponents.

Add and subtract the following monomials with exponents

10y + 9y - 17y

Solution.

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

10y + 9y - 17y =

10y^{1} + 9y^{1} - 17y^{1} =

2y^{1} = 2y

10y

2y

The answer 2y.

Example of adding and subtracting monomials with exponents.

Add and subtract the following monomials with exponents

14x^{8} + 2x^{8} - 16x^{7}

Solution.

Here 14x^{8} and 2x^{8} are like terms (monomials). We can add them

14x^{8} + 2x^{8} = 16x^{8}

The 16x^{8} and 16x^{7} are unlike terms (monomials). We cannot add them.

The answer 16x^{8} + 16x^{7}.

See the definition of unlike terms.