What is a Quadratic Monomial? (with Examples)

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 3x² – 4x³. It is a “binomial” since it consists of two terms that are separated by a minus sign.

The expression 7y³-8y²+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:

• 3x².
• 7y⁸.
• -6t³.

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 7x² – 6y² 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:

1. 7x².
2. 13y².
3. -3xy. Here, since x and y both have degree 1 the total degree adds up to 2.
4. -5st.

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

1. Coefficient – it is the numerical value that occurs before the alphabet such as the value 7 in 7x².
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 3y² and the cubic monomial 6y³. On multiplying them we get,

3y² x 6y³ = (3 x 6)(y² x y³) =18y⁵.

Now, 18y⁵ is clearly a monomial and it has a degree of 5.