Question

what is the difference between algebraic expression and polynomials?​

Answer 1

Answer:

Step-by-step explanation:

Algebraic expressions are polynomials. But all polynomials are algebraic expressions. The difference is polynomials include only variables and coefficients with mathematical operations(+, -, ×) but algebraic expressions include irrational numbers in the powers as well.

Another rule of thumb is if there are any variables in the denominator of a fraction then the algebraic expression isn't a polynomial. There are lots of radicals and fractions in this algebraic expression, but the denominators of the fractions are only numbers and the radicands of each radical are only a numbers.

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Answer 2

$\huge\underline\mathcal\orange{Polynomial}$

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

$\huge\underline\mathcal\green{Expression}$

"Algebraic 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 $\sqrt{x}$

$\huge\underline\mathcal\purple{BTS}$