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Adding and subtracting monomials with exponents

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

Examples of adding and subtracting monomials with exponents

Example of adding and subtracting monomials with exponents.

Add and subtract the following monomials with exponents

81x5 + 4x5 - 3x5

Solution.

81x5 + 4x5 - 3x5 =
82x5

The answer 82x5.

Example of adding and subtracting monomials with exponents.

Add and subtract the following monomials with exponents

3x5 + 2x5 - x5

Solution.

3x5 + 2x5 - x5 =
3x5 + 2x5 - 1x5 = 4x5

The answer 4x5.

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 =
10y1 + 9y1 - 17y1 =
2y1 = 2y

The answer 2y.

Example of adding and subtracting monomials with exponents.

Add and subtract the following monomials with exponents

14x8 + 2x8 - 16x7

Solution.

Here 14x8 and 2x8 are like terms (monomials). We can add them

14x8 + 2x8 = 16x8

The 16x8 and 16x7 are unlike terms (monomials). We cannot add them.

The answer 16x8 + 16x7.

See the definition of unlike terms.