Need help in understanding definition of monomials

Question

Wikipedia states two definitions of monomials- https://en.m.wikipedia.org/wiki/Monomial

I have understood the first one but I am facing some problem in understanding the second one which says that-" A monomial is a monomial in the first sense multiplied by a nonzero constant, called the coefficient of the monomial. A monomial in the first sense is a special case of a monomial in the second sense, where the coefficient is 1."

Someone please explain what this second definition is trying to say? And,what is this first and the second sense in this definition?

Wikipedia also mentioned this example in the second definition- For example, in this interpretation -7x^5 and (3-4i)x^4 * y*z^13  are monomials (in the second example, the variables are x,y,z and the coefficient is a complex number).

I just want to know to know what is the interpretation they are talking about?

Thanks in advanced!

Answer 1

"Interpretation", here, refers to "the meaning we give to the term 'monomial'".

The article is discussing two different possible meanings that are commonly assigned to the term. Under both, $x^3 y^7$ is a monomial. $3x^3 y^7$ is only a monomial for one of them. $x^3 + y^7$ is not a monomial for either.