# 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

**. Let's have a look at some examples.**

*literal / literal numbers*
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.*

## Algebraic Expressions

A collection of constants and literals (variables) connected by one or more arithmetic operations is called an algebraic expression. Let's see some examples.

Expression | Formation |
---|---|

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.

Expression | Terms |
---|---|

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}⁄_{3}xy 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.

## Class-6 Algebra Test

## Class-6 Algebra Worksheet

## Answer Sheet

**Algebra-Answer**Download the pdf

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