Addition and Subtraction of Algebraic Expressions

Addition and Subtraction of Algebraic Expressions Class 8

An algebraic expression is a combination of constants, variables, and operators. The four basic operations of mathematics that are addition, subtraction, multiplication, and division can be performed on algebraic expressions. The addition and subtraction of algebraic expressions are quite similar to the addition and subtraction of the numbers. However,  when it comes to the algebraic expressions, you must sort the like terms and the unlike terms together. In this article, we will learn about the addition and subtraction of algebraic expressions class 8, how to sort the like and unlike terms, and have a look at some of the solved examples.

Simplifying Expressions Of the Like and Unlike Terms

For  simplifying an algebraic expression which consists of both the like and the unlike terms, you need to follow these basic steps:

  1. Keep the like terms together.

  2. Add or subtract the coefficients of these terms.

Consider the following example:

3x + 2y - 2x + 6


= 3x - 2x + 2y + 6


= x + 2y + 6


Addition of Algebraic Expressions

In the addition of algebraic expressions when adding the algebraic expressions you need to collect the like terms and then add them. The sum of the several like terms would be the like term whose coefficient is the total of the coefficients of the like terms.


There are two ways for solving the algebra addition.

  1. Horizontal Method: 

In this method, you have to write all expressions in a horizontal line and then arrange the terms are to collect all the groups of like terms. These like terms are then added.

  1. Column Method:

 In this method, you need to write each expression in a separate row in a way that there like terms are arranged one below the other in the column. Then you need to add the terms column-wise.


Let us look at the examples using both these methods.


Add these algebraic expressions: (6a + 8b - 7c), (2b + c - 4a) and (a - 3b - 2c)


Solution: 


According to the Horizontal Method:


(6a + 8b - 7c) + (2b + c - 4a) + (a - 3b - 2c) 


Removing the terms from the brackets gives you


= 6a + 8b - 7c + 2b + c - 4a + a - 3b - 2c


Arranging the like terms together, then adding them gives you 


= 6a - 4a + a + 8b + 2b - 3b - 7c + c - 2c


Hence, the answer is 3a + 7b - 8c


According to the Column Method:


Solution:


First, write the terms of these expressions in the same order in the form of rows in a way that the like terms are below each other and the add them column-wise.


    6a + 8b - 7c


 - 4a + 2b +  c


     a - 3b - 2c

_____________

   3a + 7b - 8c

_____________


Hence, your answer is 3a + 7b - 8c.

Subtraction of Algebraic Expressions

The subtraction of algebraic expressions can be done by following these steps:


  1. First, arrange the terms of all the expressions given in the same order.

  2. The next step is to write these expressions in two rows in a way that the like terms occur one below the other. Keep the expression that needs to be subtracted in the second row.

  3. Then change the sign of every term in the lower row from - to + and from + to -.

  4. Lastly, with these new signs of the terms of the lower row, add them all column-wise. 


Consider the following example:

Subtract the expression 4a + 5b - 3c from the expression 6a - 3b + c.

Solution: 

   6a  - 3b +   c 

+ 4a + 5b - 3c 

(-)   (-)   (+) 

_____________

  2a  - 8b  + 4c 

_____________

Hence your answer is 2a - 8b + 4c.


Solved Examples


  1. Add these algebraic expressions: x + y + 3 and 3x + 2y + 5.


Solution:


To solve the addition of algebraic expressions for class 7, follow the following steps:


According to the Horizontal Method,


Add (x + y + 3) + (3x + 2y + 5)


This gives you  x + y + 3 + 3x + 2y + 5


Arranging the like terms together, and then adding gives you


= x + 3x + y + 2y + 3 + 5


= 4x + 3y + 8

According to the Column Method,


At first, arrange these expressions in lines in a way that the like terms with their signs are one below the other, that is, the like terms are in the same vertical column. Then add different groups of the like terms together.


    x + y + 3


+ 3x + 2y + 5

____________

   4x + 3y + 8


Hence, your answer is 4x + 3y + 8.


  1. Subtract 3x² - 6x - 4 from 5 + x - 2x².


Solution:


Arrange the terms of the given expressions first in the descending powers of x and then subtract them column-wise. This would give you


 - 2x² +  x + 5


 + 3x² - 6x - 4


 (-)   (+)  (+)

_____________

- 5x² + 7x + 9

_____________


Hence, your answer is - 5x² + 7x + 9.


FAQ (Frequently Asked Questions)

1. How can you add and subtract algebraic expressions?

You must be aware of the like and the unlike terms when you are adding or subtracting algebraic expressions. You can only perform the addition or subtraction on the like terms.

Like terms are the ones who have the same variables and exponents and the unlike terms are the ones that have different variables.


Consider the following example:

-5x2 + 12xy – 3y + 7x2 + xy

In this algebraic expression, the terms -5x2 and 7x2  are like terms because both of them have x2  that is a common variable. In a similar way, 12xy and xy are called the like terms.

2. Why do you change the sign in an algebraic expression while performing algebraic subtraction?

In maths, you add a negative number to an already present number and hence you change the sign. Consider the following examples:


1–2 =1+(-2)

Hence, you are removing 2 from 1 and are left with a deficit of 1 that is -1.


In the algebraic expressions, it is different if you consider 1x-2y. 

You can evaluate this if x and y are different kinds of objects, but if x=1 and y= 2 then it would be 

1(1 )-2 (2)

= 1–4 = 1+(-4)

= -3