# Basic Algebraic Concepts

**What is Algebra?**Algebra is the branch of mathematics that helps in solving equations and finding the values of variables.

**Did you know?** The word “**algebra**” is derived the from the Arabic word** ‘al-jabr’**, which means “the reunion of broken parts” (source)

**Variable**

A variable is a placeholder for various numerical values. Any letter can be used. as a variable.

x+2

A number which is the power of another variable where the power is not zero is also a variable.

x2

**Constant**

A number having a fixed numerical value is called a constant.

Example – 2,4,⅗

**Algebraic Expression**

A combination of variables and constants, connected by the fundamental arithmetic operations i.e. addition, subtraction, multiplication and division is called an algebraic expression.

Example

X+2 (sum of variable and constant)

a-9 (variable and constant are connected by subtraction)

2x-3

**Check your concept**

3y is an algebraic expression – Ture or False?

**Terms**

Various parts of an algebraic expression which are separated by – or + are called terms of the expression.

Example

4x – 2y + 6z is an algebraic expression consisting of 3\three terms.

**Coefficient of a Term**

Consider the term 6×4, 6 is called the numerical coefficient of x4 and x4 is the literal coefficient of 6.

**Like Term**

The terms having the same literal coefficient are called Like Term

3X4, 6×4,-9×4 are like terms

**Unlike Term**

The terms having the different literal coefficients are called UnLike Term

3X3, 6×4,-9×4 are unlike terms.

**Polynomial Expression**

An algebraic expression that contains one or more terms in which the variable has only non-negative integer powers is called Polynomial Expression.

Example:

x+y

x+y_z

4×2+2y+3

**Type of Polynomial Expression**

**Monomial**

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

Example

-9

7

4×2

**Binomial**

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

Example

x2 + 7

x2 – 7

x + 9

**Trinomial**

An algebraic expression that contains three terms is called a trinomial

Example

5x + 2y + 2

x2 + 5y + 3

**Quadrinomial**

An algebraic expression that contains four terms is called a quadrinomial.

Example

a2 + b2 + c2 + 3abc

ab + ac + ac + abc

**Exercise**

Find out the coefficient of each term for the below expression

x2y2 – 14x2y + 20y2x + 15xy

**Solution**

**Your Turn**

Find the coefficient of each term fpr below expression

x2y2 + 18x2y – 19y2x + 20xy

x2 – 14y

X2y2 – 14x2y40y2x + 15xy

Exercise

From the following polynomials , classify as monomials, binomials,trinimials

a+b, 21, a+b+c, 45, x2-y2

Solution

Monomials – 21 , 45

Binomials – a+b , x2-y2

Trinimials – a+b+c

Your Turn

From the following polynomials , classify as Monomials, Binomials,Trinimials

x+y, 35, x+y+z, a+b+100