express this in binomial:

2
4ez (4e-z)

the 2 is the square..

can anyone teach me how to do this???

I'm a little unsure what your question is asking for here. Ordinarily, a binomial is an expression with two variables and some positive power, e.g.
(x+y)^2 or (x+y)^3
are expressions where we would use the binomial theorem to determine the coefficients of the expanded product.
This part right here
4ez (4e-z)
is already in simplest terms. If you were to distribute it you'd get
4(e^2)z-4ez^2
This is just the distributive property. I only put the parentheses around e so there's no confusion here; if you write this on paper they can be omitted.
I'm not sure if this answers your question or not. If not, please repost it with a little more explanation of what's being sought.

you are completely wrong about what a binomial is.

MONnomial : one factor 2 or 2xy^3
BInomial: two 2+2 or 3x^2+2y^4
POLInomial : three+ 2+x+8+v+q or 1+t+uv

Ok, I'll take your word on this. Let me point out that I've taken a significant amount of college math and the only terms I know (with certainty) that are used frequently are binomial (in the sense I gave) and polynomial, which is defined several ways. Multinomial is also used, but only as a generalized binomial.
All of the examples you gave are polynomials since they involve experssions in two or more variables.
You defined monomial as a single factor; more often we're concerned with the number of variables, not just the number of terms. But an expression in a single variable would still be called a polynomial, sometimes a factor, other times simply a term.
Hopefully you see that a little more explanation is needed to make sense of the original question.

I apologize for the confusion earlier. Now that I understand what you're asking for, I can help you express your expression in binomial form.

To express an expression in binomial form, we need two terms connected by an operation such as addition or subtraction. In your case, we have the expression 4ez (4e-z).

To express this as a binomial, we can simplify it by multiplying the two terms together:

4ez * 4e-z = 16e^2z * e^-z

Simplifying further, we can combine the same base (e) by adding the exponents:

16e^2z * e^-z = 16e^(2-1)z = 16ez

Therefore, the expression 4ez (4e-z) can be expressed as the binomial 16ez.