Class 6 Algebra
Introduction to Algebra
It is branch of mathematics in which we use literal numbers and statements symbolically. Literal numbers can be positive or negative, they are variables.
Constant and Variables
In algebra, we use two types of symbols, that is constants and variables.
A symbol which has a fixed value is known as Constant. For example 5, -2, 0, 2⁄5, 5⁄3, etc. are constant.
A symbol (letter) which can be given various numerical values is known as variable. As variables are usually denoted by letters, so it is also known as literal / literal numbers. Let's have a look at some examples.
In 2n, 2 is constant and 'n' is variable. But, together 2n is a variable.
When n = 1, 2n = 2 x 1 = 2
When n = 2, 2n = 2 x 2 = 4
When n = 3, 2n = 2 x 3 = 6
So, when 'n' takes various values , 2n also change accordingly.
Similarly, n + 2, n −3, 5 −n , 2⁄n and n⁄5 are variables.
Hence a combination of constant and variable is also a variable.
A collection of constants and literals (variables) connected by one or more arithmetic operations is called an algebraic expression. Let's see some examples.
|a + 2||2 is added 'a'|
|b − 5||5 is subtracted from b|
|3n||3 is multiplied by 'n'|
|n⁄5||'n' divided by 5|
|−4y||−4 is multiplied by 'y'|
|5n + 3||First 'n' is multiplied by 5 then 3 is added to the result|
Terms of Algebraic Expression
The various part of an algebraic expression separated by + / − sign are known as terms of the algebraic expression. Let's have a look at some examples.
|3a + 5b||3a, 5b|
|3n + 7m²||3n, 7m²|
|2x − y⁄5||2x, − y⁄5|
|2x + 4y² − 5||2x, 4y², − 5|
Coefficient of a Term
Any factor of a term of an algebraic expression is called coefficient of the remaining factor of the term. Let's see some examples.
Let's consider the below given expression.
6abc + 4ab² − 4
In the term 6abc,
Numerical coefficient = 6
Literal coefficient = abc
Coefficient of a = 6bc
Like and Unlike Terms
The terms having same literal coefficients are called like terms, otherwise, the terms are called unlike terms. Let's see some examples.
2xy, 3xy, 4xy, 5xy, −xy, 2⁄3xy are like terms.
2m, 4mn, 3m²n are unlike terms.
Polynomials in one variable
An algebraic expression of the form a + bx + cx² + ..., where a, b, c, ... are constants and 'x' is a variable, is known as a polynomial in the variable 'x'. Let's see some examples.
i) 3 + 4x is a polynomial in 'x' of degree 1.
ii) 2 − 3y + 5y² is a polynomial in 'y' of degree 2.
Degree of a Polynomial
The degree of each term in a polynomial is the sum of the exponents of variables of the term and the degree of the polynomials is the greatest of the degrees of its terms. Let's see some examples.
Example 1. Find out the degree in the given polynomial.
3 + 4x
Solution. In 3 + 4x, the degree of two terms 3 and 4x are 0 and 1 respectively. The degree of the polynomials is 1.
Example 2. Find out the degree in the given polynomial.
5y² + 3y − 2
Solution. In 5 y² + 3y −2, the degree of 3 terms 2, 1 and 0 respectively. So, the degree of the polynomial is 2.
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