Formulas obtained by finite algebraic operations such as addition, subtraction, multiplication, division, multiplication and square root of numbers and letters representing numbers or mathematical expressions containing letters are called algebraic expressions. In the range of real numbers, algebraic expressions can be divided into rational number expressions and irrational number expressions.
Category of algebraic expressions
rational expression
Rational expressions include algebraic expressions and fractions. In this algebraic expression, only a limited number of operations such as addition, subtraction, multiplication, division and integer idempotency are performed on letters.
Integral expression
Monomial: Algebraic expressions without addition and subtraction are called monomials.
Polynomial: the algebraic sum of several monomials is called polynomial; Each monomial in a polynomial is called a polynomial term. Items without letters are called constant items.
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Generally speaking, if A and B(B is not equal to zero) represent two algebraic expressions, and B contains letters, then the formula A/B is called a fraction, where A is called a numerator and B is called a denominator. Fraction is an algebraic expression different from algebraic expression, and its value changes with the change of letter value in fraction.
Irrational formula: We call the formula that contains the radical of letters, the non-integer power of letters, or the non-algebraic operation as irrational formula. We call an algebraic expression that can be transformed into a rational expression and the root index has no letters a radical.