Addition and Subtraction of Algebraic Expressions

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 numbers. However,  when it comes to 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 in class 8, how to sort the like and unlike terms, and have a look at some of the solved examples.

The scope of this topic is not limited to schooling level as it keeps high importance in the competitive examinations as well. We have compiled the entire subject with the help of a few examples and easy to understand definitions. All the basic formulas have been covered here to prepare them from the initial days. Here you go with the definitions, examples, and sample questions. Best of luck with the preparation you go ahead with.

Simplifying Expressions Of the Like and Unlike Terms

For simplifying an algebraic expression, which consists of both like and 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, 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 to collect all the groups of like terms. These like terms are then added.

2. Column Method:

In this method, you need to write each expression in a separate row in a way that their 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 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,

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.

2. 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.

Conclusion: 

You need to brainstorm to get an appropriate answer for them. In simple terms, the trinomials and polynomials have also been defined. If you understand and know the basic root of all such terms, then you are sure to take your mathematics computation to the next level. With great preparation from grade 8 onwards, you can start dreaming of becoming a part of the top examinations such as Banking, GATE, CAT, IAS, etc as these also have a good weightage of algebra.