Basic Algebraic Concepts

In this article, we are going to learn about algebra basics concept such as variable, constant, algebraic expression, terms, like terms, unlike terms, Coefficient of a Term etc. 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

algebra_basics

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

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