Question

Do all polynomials have only one variable? What's the difference between algebraic expression and polynomials?

Answer 1

No. A polynomial can have more than one variable.
for example 2x+4y =1 is a polynomial in two variable.


Polynomial" is a precisely defined term. A polynomial is constructed from constants and variables by adding and multiplying. One could add "subtracting", but x−yx−y is x+(−1)yx+(−1)y, so adding and multiplying are enough.


"Alebraic expression" is not a precisely defined term. Algebraic expressions include many things that are not polynomials, including rational funtions, which come from dividing polynomials, and things like x−√x.