Algebra

Power with natuarl exponent: If a is a real number and n is a natural number different from unity, then the prduct of n factors, each of wich is equal to a, is called the nth power of the number a and is denoted by aⁿ; if n=1, then we set a¹=a.

{aⁿ ½ a � R, n N \ {1}}

The number a repeated as a factor is called the base of the power, and number n which indicates how many times the base is to be used as a factor is called the exponent of the power. The result is called the power.

Monomial is such an expression wich contains numbers, variables (letters), powers of numbers and variables, and their products. e.g.: 2a*8b³*5²

The fundamental law of algebra is to reduce the monomial to the standard form.

Standard form: it is such a form where numbers are multiplied by variables on the suitable power in alphabetic order

2 monomials are similar if they differ only in the coefficients.

Collecting like terms: the addition and substraction of similar monomials.

Identity: and equality whose left and right sides are identically equal expressions.

Polynomials: it is defined as the sum of monomials.

Standard form of polynomials: a polynomial is in standard form when the monomials in it are in standard form.

Factorisation of polynomials into factors: the representation of a polynomial in the form of a product of a number of polynomials among which some monomials may also encounter.