Division of Algebraic Expression-

An algebraic expression is a type of mathematical expression in which numbers and variables are used to represent some formula or expression. There are four main types of operations in an algebraic operation such as addition, subtraction, multiplication, and division of algebraic expression. An algebraic expression contains variables and constants. These expressions are using the fundamental operations and fundamental formulas of algebra or mathematics. These expressions have been divided into three types, monomial expression, binomial expression, and polynomial expression. These expressions have been classified based on the highest power of the variables. In order to divide the expressions, they may be of any form, such as monomial, binomial, or polynomial. 

3. Discussion

3.1 Formula for division of algebraic expression

In order to do some operations with algebraic operations, there are four main types of operations that are being done with algebraic expressions. The operations are the addition of algebraic operation, subtraction of algebraic operation, multiplication of algebraic operation, and division of algebraic operation. The first two operations can be done only with the same type of expressions. Such that a variable of power two cannot be added or subtracted with a variable with power one. But in the case of multiplication and division, any type of expression can be multiplied or divided with any type of expression. While conducting the multiplication and division operations for algebraic expressions, the formula of indices or exponents has been followed. These are the basic and fundamental formulas of mathematics. That is used in these operations. While dividing x4x2 these types of expressions, fundamental formulas of indices have been used. The main formula behind this isaman= am-n. Using this fundamental formula of exponent, most of the algebraic expressions have been divided. In order to conduct the whole division of algebraic operations such as 2x3+3x2+10x+5 by the algebraic operation2x+1. Some particular quotient and remainder will come. After dividing these expressions, x2+2x+4 is the quotient, and 1 is the remainder. 

3.2 Definition for division of algebraic expression

Great mathematician Euclid has stated the division formula, which is the main fundamental formula for the division. Euclid has used four terms to define the division algorithm. The four terms are dividend, divisor, quotient, and remainder. The algorithm using these four terms is dividend = divisor x quotient + remainder, where 0≤remainder<divisor

. This algorithm is known as Euclid’s division algorithm. This is the fundamental formula of the division operation. Mathematicians have used some specific notation for representing the terms in Euclid’s division algorithm. The terms are denoted by some alphabets. Such as dividend is denoted by a divisor is denoted by b, the quotient is denoted by q, and the remainder is denoted by r. Euclid’s division algorithm is also stated as a=b×q+r, where  0≤r<b. Using this fundamental formula of division, most divisions have been done. This formula is mainly used for dividing a single term by a single term. In the case of algebraic expression, the Euclid algorithm is stated as 2x3+3x2+10x+5=x2+2x+42x+1+1. While dividing the whole expression, according to the dividend, the divisor is multiplied with a specific value, that may be constant or variable to eliminate the first term of the dividend. After that, the term is subtracted and put in the remainder. In order to find a result of the division, this process is followed until the remainder is greater than or equal to zero and strictly less than the divisor. 

3.3 Application for division of algebraic expression

There are so many applications of the division of algebraic expressions. Since division is a binary operation, it has so many uses and applications. The operations which are using only two operands are called binary operations. The fundamental operations such as addition, subtraction, multiplication, and division all are binary operations. Since all the operations are operated with only two operands. Since division is a binary operation; there are so many applications and uses of this division algorithm. Math is a backend of all types of streams. In order to conduct any type of calculation, a division is required. Hence, in many fields such as physics, chemistry, accounts, economics, and business, mathematical operations are always used by all. In order to find some distribution calculation, the division is the best method to find the solution to such a distribution problem.  As an example, 10 chocolates have to distribute among 5 people. So, dividing the number of chocolates by the number of people. Hence, all of them will get 2 chocolates. All of them can gave the same number of chocolates. This can be possible by the division operation. The division is not only used for doing this small calculation. It is also useful for dividing big numbers by some other huge numbers. It also includes division of floating-point numbers which means decimal point divisions. Besides these, division operation has so many applications and uses in many fields. 

4. Conclusion

The division operation uses Euclid’s division algorithm. Using this algorithm there are so many uses and applications that are discussed in the above sections. The corresponding formulas and the definitions of the division algorithm have also been discussed in the above sections. This assessment consists mainly of the operation including the division of algebraic expressions. Using the fundamental division formula and fundamental formulas of exponents or indices, the division provides very ease to the students and many others. Based on the formulas, there are so many advantages and applications of the division operation in mathematics and in other fields too.