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:
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:
- -3xy. Here, since x and y both have degree 1 the total degree adds up to 2.
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 7x2.
- 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.