How to subtract unlike monomials? How do you subtract unlike monomials?

We can only subtract like terms (monomials) and we cannot subtract unlike terms (monomials).

See the definition of like terms.

See the definition of unlike terms.

Like terms are monomials that can only differ in their coefficients.

Subtracting monomials example.

Subtract the monomials

13x - 10x

Solution.

13x - 10x = 3x

Here two monomials have got the same literal part. That is why we can subtract these two monomials. The coefficients (13 and 10) are not equal but that does not matter.

Example of subtracting monomials.

Subtracting monomials

42y - 22y - 2z

Solution.

Here 42y and 22y are like terms. We can subtract them

42y - 22y = 20y

20y and 2z are unlike monomials (terms). We cannot subtract them.

So

42y - 22y - 2z =

20y - 2z

20y - 2z

Example of subtracting monomials.

Subtract the following monomials

5.6y - 1.5y - z

Solution.

Here 5.6y and 1.5y are like terms. We can subtract them

5.6y - 1.5y = 4.1y

4.1y and z are unlike monomials (terms). We cannot subtract them.

So

5.6y - 1.5y - z =

4.1y - z

4.1y - z

Example of subtracting monomials.

Subtract the monomials

17y^{5} - 15y^{5} - 2z^{5}

Solution.

Here 17y^{5} and 15y^{5} are like terms. We can subtract them

17y^{5} - 15y^{5} = 2y^{5}

2y^{5} and 2z^{5} are unlike monomials (terms). We cannot subtract them.

So

17y^{5} - 15y^{5} - 2z^{5} =

2y^{5} - 2z^{5}

2y