What are names of algebraic expressions? What is name of algebraic expressions having many terms? Basically I have doubt about the use of word polynomial=many terms.
Sometimes books say algebraic expressions having many (or any number of)terms are polynomial.
E.g 5/x is monomial expression.
5/x+ 7y is binomial expression
Then books say terms of polynomials can't have negative or fractional powers but terms of algebraic expressions can have.
e.g. 5x is monomial but 5/x is not.
The above two things are confusing. what is correct terminology for algebraic expressions having 1 term or 2 terms or many terms?

AFAIK there is no specific terminology for an algebraic expression having $1$ term or $2$ terms or many terms.  I'd just say "an algebraic expression having $\ldots$ terms."
"Many terms" for a polynomial is etymology, not definition.
A polynomial is not just any kind of algebraic expression: a polynomial in variable $x$ is a sum of one or more terms consisting of a coefficient (which does not depend on $x$) times a nonnegative integer power of $x$.
