algebra definations of algebra

In algebra, we come  across two types of symbols namely constants and variables.

Constant :-  

A symbol having  fixed numerical value is called a constant

Variable or a Literal :- 

A symbol which can take  various numerical values is called a variable or a literal

                  A symbol which takes on various numerical values is called a variable or a literal

Which is the product of a constant and a variable is also a variable.

EX:  3x,  -5y etc.,

A combination of two or more variables separated by + sign or  – sign is also a variable.

Constants:  

A symbol having  fixed numerical value is called a constant.

In fact, every number is  constant.

TERMS: A constant or a variable or the product of a constant and a variable is called a term.

Product of two or more terms is also called a term.

Every constant or variable is called a term.

3x.y   

ALGEBRIC EXPRESSIONS:

A combination of constants and variables, connected by the symbols  is called an algebraic expression.

The several parts of an expression separated by the sign   are called the terms of the expression.

A single term or a group of terms with addition and subtraction operations is called an expression 

If every term of an expression is a constant term, such expression is called numerical expression.

Every numerical expression represents a number.

The expression containing at least one algebraic term is called an algebraic expression.

Types of Algebraic Expressions:

Algebraic expressions are categorized according to the number of 

terms in it.

     An algebraic expression which contains only one term is called a monomial.

      An algebraic expression which contains two terms  is called a binomial.

      An algebraic expression which contains three terms is called a trinomial.

      An algebraic expression which contains two or more terms  is called a multinomial.

Factors of  term:

When numbers and literals are multiplied to form a product, then 

each quantity multiplied is called a factor of the product.

A constant  factor is called  numerical factor while a variable 

factor is called a literal factor.

In 7ab, 

the numerical factor is 7 

and the literal factors a, b and ab

In 

, the numerical factor is and the literal factors x, 

constant term : A term of the expression having no literal factor is 

called the constant term

In the expression , the constant term is 7

Coefficients:-  

In a product of two or more factors, every factor is called the coefficient of the product of the remaining factors.

If the coefficient is a number then it is called numerical coefficient and if it is literal term, then it is called literal coefficient.

In particular, the constant part is called the numerical coefficient of the term and remaining part is called the literal coefficient of the term

Examples:  In the term 

Note:  If the numerical coefficient is  these will not be written.

Generally numerical coefficient is used as coefficient of that term

Like terms: The terms having same literal factors(coefficient)  are called  like terms or similar terms

Unlike terms: The terms not  having same literal factors are called unlike terms or dissimilar terms

The terms having different literal coefficients  are called unlike terms or dissimilar terms

The terms having same literal factors are known as like terms. Otherwise they are known as unlike terms.

If the like terms are added or subtracted (that means if the addition and subtraction operations are applied  and simplified, then the result becomes the same kind of like terms.

The simplification of like terms will be complete only when the coefficients of the like terms of the expression are simplified.