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 addds up to 2.
- -5st .

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

- Coefficient – it is the numerical value which 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 to 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 \times 6y^3 = (3 \times 6)(y^2 \times y^3) =18y^5. Now 18y^5 is clearly a monomial and it has degree 5.