What is the difference between the polynomial and multinomial?

Any sum of one or more terms is called a Polynomial. Polynomials have different names.

for example

x is a monomial*

x+1 is a binomial

x-1+y is a trinomial

x-1+y+2x is a multinomial (could have been called quadnomial but ... lol nah)

So what is a Quadratic? It is just a polynomial where the highest exponent (power) is 2. Basically, a polynomial of the 2nd degree algebraically.

For example,

x²+y-3 is a quadratic trinomial

x² is a quadratic monomial

*by the way if you are wondering what makes a term like x or x² a sum or a polynomial when there is nothing else you see that is being added or taken away then see this ...

x = x + 1 - 1

x² = x² + 1 - 1