Basic Algebraic Concepts
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