Question

Is 4x2y2 an example of a binomial or a trinomial and what is the degree?

Answer 1

4x²y² is an example of monomial. It's neither an example of binomial nor trinomial.

Because binomial is a type of polynomial which has two terms in it.

And trinomial is a type of polynomial which has three terms in it.

But here, there's only one term.

$\fbox{\bold{\mathsf{Note:}}}$

Terms are separated by mathematical operations such as plus (+) and minus (-).

They aren't separated by division (÷) and multiplication sign (×).

If the given term was like this: 4x² + y² then it would be considered as a binomial as it has two terms in it which are separated by a mathematical operation - plus (+).

If the given term was like this: 4x² - y² then it would be also considered as a binomial as it has two terms in it which are separated by a mathematical operation - minus (-).

But here the given term is in multiplication so, it would be considered as a monomial as multiplication sign (×) doesn't separate the terms. It can be also expressed as 4x² $\times$ y².

If it would be written like this: $\mathsf{\frac{4x^2}{y^2}}$ then it would be also considered as a monomial as division sign (÷) doesn't separate the terms.

So, 4x²y² an example on monomial.

As we know, degree is the highest power of a polynomial.

If a polynomial has only one variable then the degree will be the highest power of the term. But if the variable has more than two variables so, we have to add all the powers to get the degree.

Here, 4x²y² has two variables so we have to add up the powers.

Adding powers we obtain,

2 + 2 = 4

So, the degree of 4x²y² is 4.