Addition of Algebraic expressions

Addition of algebraic expression is a general operation on algebraic expression in which two or more algebraic expressions are added to find one simplified expression. For the addition of Algebraic expressions, two methods are used:

• Horizontal Method
• Column Method

Now let’s learn them in detail.

Horizontal Method

There are several steps which need to be followed while implementing the Horizontal method

Step 1. First of all, we write all the algebraic expressions with the help of addition symbol.

Step 2. Now, we open the brackets and multiply the signs.

Step 3. After step 2, we gather the similar terms and place them at one place.

Step 4. Now, add the similar terms by adding the coefficients.

These steps are explained using some example as added below:

Example 1: Add the following Algebraic expressions: 5x + 3, 6x + 9, -4x – 5

Solution:

(5x + 3) + (6x + 9) + (-4x – 5)

= 5x + 3 + 6x + 9 -4x -5

= (5x + 6x – 4x) + (3 + 9 -5)

= 7x + 7

Example 2: Add the following Algebraic expressions: 4x + 6y – 5, 10x – 8y + 12, -2x + 3y + 2

Solution:

(4x + 6y – 5) + (10x – 8y + 12) + (-2x + 3y + 2)

= 4x + 6y – 5 + 10x -8y + 12 -2x + 3y + 2

= (4x + 10x -2x) + (6y -8y + 3y) + (-5 + 12 + 2)

= 12x + y + 9

Example 3: Add the following Algebraic expressions: 4x² + 5x + 6y – 5, x² + 10x – 8y + 12, -2x² -2x + 3y + 2

Solution:

(4x² + 5x + 6y – 5) + (x² + 10x – 8y + 12) + (-2x² – 2x + 3y + 2)

= 4x² + 5x + 6y – 5 + x² + 10x -8y + 12 -2x² – 2x + 3y + 2

= (4x² + x² -2x²) + (5x + 10x -2x) + (6y -8y + 3y) + (-5 + 12 + 2)

= 3x² + 13x + y + 9

Column Method

To add algebraic expressions using Column method, arrange the similar terms in the same column and then add them accordingly. This concept is explained in the example below.

Example 1: Add the following Algebraic expressions: 4x + 3, 8x + 9, -6x – 5

Solution:

Now adding first column and second column individually

So, the result is 6x+ 7

Example 2: Add the following Algebraic expressions: 4x + 6y – 5, 10x – 8y + 12, -2x + 3y + 2

Solution:

Now adding first column and second column individually

So, the result is 12x + y + 9

Example 3: Add the following Algebraic expressions: 4x² + 5x + 6y – 5, x2 + 10x – 8y + 12, -2×2 -2x + 3y + 2

Solution:

Now adding each column individually

So, the result is 3x² + 13x + y + 9.

Addition and Subtraction of Algebraic Expressions are fundamental operations performed on algebraic expressions. These operations are used to simplify algebraic expressions. Let’s learn in detail about Algebraic expressions, addition of algebraic expressions, subtraction of algebraic expressions and others in detail.