A quadratic monomial is an algebraic expression that consists of a single expression of degree two.

- The word “monomial” stands for the fact that there is only one term.
- The word quadratic means that the term has degree 2.

Let us first try to understand the meaning of the terms – “monomial” and “quadratic”.

**What is a Monomial?**

Consider the algebraic expression 3x^{2} – 4x^{3}. It is a “binomial” since it consists of two terms that are separated by a minus sign.

The expression 7y^{3}-8y^{2}+13y is a “trinomial” since it consists of three terms that are separated by a plus or minus sign.

On the other hand, an expression of the form 3x^2 is a monomial since it consists only of a single term. Some examples of monomials are:

- 3x
^{2}. - 7y
^{8}. - -6t
^{3}.

**What do we mean by Quadratic?**

By a quadratic expression, we mean an expression where the total degree of each term adds up to two.

For example, the expression 7x^{2} – 6y^{2} is quadratic since both x and y have degree 2.

Similarly, the expression 3xy is quadratic since we have an x variable of degree 1 and a y variable of degree 1, and hence the total degree adds up to 2.

**Examples of Quadratic Monomials:**

A quadratic monomial is an algebraic expression consisting of a single term of degree two. Some examples of quadratic monomials are:

- 7x
^{2}. - 13y
^{2}. - -3xy. Here, since x and y both have degree 1 the total degree adds up to 2.
- -5st.

From the above examples, we see that a quadratic monomial consists of two parts:

- Coefficient – it is the numerical value that occurs before the alphabet such as the value 7 in 7x
^{2}. - Variables – There are the alphabets that occur in our expression such as xy in the expression -3xy.

**What happens if you multiply a quadratic monomial by a cubic monomial?**

If we multiply a quadratic monomial with a cubic monomial then we get a monomial whose total degree is equal to 5.

For example, consider the quadratic monomial 3y^{2} and the cubic monomial 6y^{3}. On multiplying them we get,

3y^{2} x 6y^{3} = (3 x 6)(y^{2} x y^{3}) =18y^{5}.

Now, 18y^{5} is clearly a monomial and it has a degree of 5.