Subtraction of Algebraic expressions

Subtraction of algebraic expressions fundamentally subtracting various algebraic expression accordingly to find one simplified expression. For the subtraction of lgebraic 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 Subtraction 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, subtract the similar terms by subtracting the coefficients.

Example 1: Subtract 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)

= 3x – 1

Example 2: Subtract 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)

= -4x + 11y -19

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

= 5x² -3x + 11y -19

Column Method

To Subtract algebraic expressions using Column method, arrange the similar terms in the same column and then subtact 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 subtracting first column and second column individually

So, the result is 2x – 1

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

Solution:

Now subtracting each column individually

So, the result is -4x + 11y -19

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

Solution:

So, the result is 5x² – 3x + 11y – 19.

Read More:

• Algebra Formulas
• How are Algebraic Expressions Formed?
• Division of Algebraic Expressions
• Multiplication of Algebraic Expression

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.