Operations on Algebraic Expression

Algebraic operations are the type of operations that consists of three major parts called variables, coefficients and constants. There are also four basic operations namely addition; symbolised by “+”, subtraction; symbolised by “-”, multiplication; symbolised by “*” and division; symbolised by “/”.  Operations are the process through which complex and simple equations can be solved by minimal efforts. There are three types of algebraic expressions called  monomial, binomial, trinominal and polynomial. Polynomial can also be called multinomial due to its calculation of multiple linear equations simultaneously. In the following, all the aspects of algebraic expression have been discussed with appropriate examples and understanding.

Types of Algebraic Expression

Before delving into major aspects of the operations of the algebraic expressions, it is important to consider the terms of algebraic expression. There are three basic algebraic terms such as variables, coefficients, and constants. Variables comprise the expression of alphabetic letters included with integers or fractions or other alphabetic letters alone such as 8xyz. Coefficients are numbers aligned with the associated variables in a single term such as 25x+12y+9. Constants are numbers or sometimes integers that are generally connected with other terms by basic operations such as 3a+2b+5c. Algebraic expressions are categorised into three parts: monomial, binomial and polynomial. Monomial or single term expression of algebraic can be exemplified as 3ab, 7p, 5xyz and so on. Where the letters are variables and the digits are the coefficients. A binomial or two-term algebraic expression can be exemplified as 2xy−x. A polynomial or multi-term algebraic expression can be exemplified as 2x+5y−4. 

Order of Operations

Certain orders are followed in the algebraic expressions to be worked on desired lines. It becomes easy to solve the algebraic expression by breaking down the whole expression and solving accordingly. Utility acronym “BODMAS” can be recalled to arrange the expression in an appropriate order. Here, B stands for brackets. That is parenthesis needed to be solved at first. O depicts the ‘of’ which are operated after the brackets. D indicates the division which is to be done after the exponents. M, which indicates multiplication, needs to be solved after the division has been done. It comes in the fourth operation of the algebraic expression. Then comes the A, which stands for the addition at the fifth operation and must be solved after the multiplication is done. Finally, the operation of S indicates subtraction needs to be solved to get accurate results after solving the algebraic operation.

Fundamental Operations

Mathematical operations performed on numbers can also be performed on algebraic expressions. 

In addition, subtractions, multiplication and division using numbers are the same as algebraic expressions. In algebraic expressions, grouping like and unlike terms together and simplifying is the essential method for solving the equation. It involves the properties such as the distributive and commutative property of addition which make the calculation convenient during the multiplication of the polynomials. Division in the algebraic expression can be done by dividing two whole numbers or fractions. Taking out of the common terms and cancelling out the same has been adopted while two algebraic expressions or variables are considered. These common terms may include constant, variables or coefficients. Now, four fundamental operations of algebraic expression have been discussed such as addition, subtraction, multiplication and division.

The addition of algebraic expressions follows some steps. In the first steps, based on the variables, sorting out the like terms takes place. That is, the same variable consisting of terms are grouped. The second step, addition takes place on all the grouped terms which comprises of the same variables. After that, all the coefficients are added and written in a single coefficient term. The same has been done with all the likes. For the constants, usual additions are adopted to form a single constant term. In the situation when no likes are found, the algebraic expression should be kept as it is. In the operation of subtraction of algebraic form, one should emphasise more on the signs during subtracting one expression from the others. For example, if a subtraction sign is located before the brackets, all the signs inside the bracket must be reversed. It is also recommended to use column subtraction methods. It is further divided into two parts as horizontal and column methods. Multiplication algebraic expression follows some steps which are discussed below. In the first step, multiplication is done by multiplying each term of the first expression with each term of the second expression. In the second step, if the same variables are appearing, add the power and express the exponent with that of variables. After that, in cases of different variables that exist in the expression, one can write them as the product of another variable. Respective signs should be allocated to separate every term obtained after the multiplication. The same steps are also followed in the case of divisions.

Conclusion 

It has been seen that all the operations of the algebraic expression follow some specific steps to produce accurate results. For example, in the case of an addition, there are four major steps to be followed for the calculation. The same is done for the other operations such as subtractions, multiplication and divisions. Apart from that, explanation and the application of various operations on various types of algebraic operations has also been discussed such as monominal, binomial, trinomial and polynomial. This specification of the algebraic expression has its value proposition in the realm of mathematics and must be treated specifically.