STD VIII – ALGEBRA (Hybrid)

Algebraic Expressions

In Mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).

Identities

An equality, true for every value of the variable in it, is called an identity

Factorization

Factors of natural numbers

We can take a natural number and write it as a product of other natural numbers which are called factors of the natural number

Factors of algebraic expressions

In algebraic expressions, terms are formed as products of factors

◦ For example, in the algebraic expression 5xy + 3x the term 5xy has been formed by the factors 5, x and y

Linear Equations In One Variable

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable (however, different variables may occur in different terms).

The constants may be numbers, parameters, or even non-linear functions of parameters, and the distinction between variables and parameters may depend on the problem