Subtraction of Algebraic Expressions

Subtraction of Algebraic Expressions refers to combining like terms together and then subtracting their numeral coefficients. Subtracting algebraic expressions involves combining like terms with attention to the signs. Subtraction of algebraic expression is a widely used concept used for problem-solving.

👁 Subtraction-of-Algebraic-Expressions

In this article, we will learn the concept of Subtraction of Algebraic Expression and different rules and methods to perform subtraction of algebraic expressions.

Algebraic Expression

An algebraic expression is an expression composed of various components, such as variables, constants, coefficients, and arithmetic operations. These components form various parts of the algebraic expressions. They are the building blocks of equations and inequalities, representing unknown quantities (variables) and known values (constants) with various mathematical operations.

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• Algebraic Expressions

Subtraction of Algebraic Expressions

Subtraction of algebraic expressions involves subtracting one expression from another. The expression which is subtracted is known as subtrahend and the expression from which the subtrahend is subtracted is known as minuend.

Subtraction can only be carried out between like terms, so the first step required for subtracting two expressions is combing the like terms together and then performing the subtraction operation. Subtraction of algebraic expressions involves finding the difference between two expressions.

How to Do Subtraction of Algebraic Expression?

Subtraction can be carried out between like terms only. Subtracting algebraic expressions follows specific rules and methods which are explained below:

Rules for Subtracting Algebraic Expressions

Following are rules for subtracting algebraic expression:

Flip Signs: When subtracting an expression, always flip the signs of every term in the second expression and then perform addition. For instance, subtracting (2x from 3x) is like adding [2x +(- 3)].

Combining Like Terms: Group like terms together, as the subtraction operation can be performed upon like terms only. For example, 2x² and 5x² are like terms, while 3x and 2y are unlike terms.

Simplifying Result: After combining like terms, you might have some non-like terms remaining. Simply combine these leftover terms into a single expression to get your final answer.

Method to Do Subtraction of Algebraic Expression

Subtracting algebraic expressions can be done by two methods namely:

• Horizontal Method
• Column Method

Below is the explanation of each method with examples of each method is given below:

Horizontal Method

Follow the below given steps to subtract algebraic expressions by horizontal method:

• Align Terms: Write both expressions next to each other, ensuring terms with the same variables and exponents are lined up horizontally.
• Group and Subtract like Terms: For each group of like terms, simply subtract the coefficients (numerical parts). Remember to keep the variable part and exponent the same.
• Combine simplified Terms: Once you've subtracted all like terms, collect the remaining terms into a single expression.

Let us take an example for the same

Example: Subtract 3x² + 2x - 5 from 5x² - 4x + 1 by horizontal method.

Solution:

Step 1: Align terms

(5x² - 4x + 1) - (3x² + 2x - 5)

Step 2: Group and Subtract like terms

(5x² - 3x²) + (-4x - 2x) + (1 + 5)

Step 3: Combine simplified terms

2x² - 6x + 6

Column Method

To subtract algebraic expressions by column method follow the below given steps:

• Write expressions vertically: Place each expression one below the other, aligning terms with the same variable and exponent in the same column. Add extra rows of zeros if needed to make all columns equal in length.

• Change the sign in the last row: Flip the operator (sign) of the second expression in the column.

• Subtract coefficients: In each column, subtract the corresponding coefficients from the top expression from the one below. If a column only has one term, simply write that term in the result row.

• Write the simplified expression: Combine all terms in the result row. Similar to the horizontal method.

Let us take an example for the same

Example: Subtract (2a² + 3b) - (a² - 2b).

Solution:

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Operations on Algebraic Expressions

Algebraic expressions are the foundation of mathematical equations and requires various operations to be carried out for problem solving and to find the solution for the given equation. The four basic operations of Algebra are:

• Addition
• Subtraction
• Multiplication
• Division

Addition: Addition combines two expressions by adding their corresponding like terms. Remember, "like terms" are those with the same variable(s) raised to the same power:

Example: Combine 2x + 5y and 3x - 2y.

Identify like terms (x and y).

Add coefficients: (2x + 3x) + (5y - 2y) = 5x + 3y.

Subtraction: Subtraction finds the difference between two expressions by subtracting corresponding terms, often reversing signs in the second expression.

Example: Subtract 2x² + 5x from 4x² - 3x.

Change signs: 2x² + 5x becomes -2x² - 5x.

Subtract: (4x² -2x²) + (-3x - 5x) = 2x² - 8x.

Multiplication: Multiplication combines expressions using the distributive property: multiply each term in one expression by each term in the other and add the products.

Example: Multiply (x + 3) by 4.

Given Expression: (x + 3)

Multiply by 4: 4 × x + 4 × 3

= 4x + 12

Division: Division refers to dividing a given expression by the other. It can involve various techniques depending on the expressions, an example of division of algebraic expression is:

Example: Divide 6x² + 12x by 3x.

Given, (6x² + 12x ) ÷ 3x

(6x² ÷ 3x) + (12x ÷ 3x)

= 2x + 4

Also Read

• Types of Algebraic Expression
• Algebra

Examples of Subtraction of Algebraic Expression

Example 1: Subtract 3x² + 2x from 4x² + 7y.

Solution:

We have, 4x² + 7y -(3x² + 2x)

Change the sign of the term to be subtracted, we get

4x² + 7y- 3x² - 2x

Combine like terms and than subtract the coefficients of similar terms.

(4x² - 3x² + 7y - 2x)

 = x² + 7y -2x

Example 2: The perimeter of an isosceles triangle is 10xy+ 3y²+ 4x². If the length of equal side is 4xy+ x². Find the other side of the triangle.

Solution:

Length of equal side = 4xy+ x²

Perimeter of triangle = sum of all three sides = 10xy+ 3y²+ 4x²

We have,

4xy+ x² + 4xy+ x² + third side = 10xy+ 3y²+ 4x²

8xy + 2x² + third side =10xy+ 3y²+ 4x²

Hence, third side = 10xy+ 3y²+ 4x² - 8xy + 2x²

Third side = 2xy + 3y²+ 2x²

Example 3: Subtract 2y² + 3x² + 3yx from 5x² + 4y²

Solution:

We have, 5x² + 4y² -(2y² + 3x² + 3yx)

Change the sign of the term to be subtracted, we get

5x² + 4y² - 2y² - 3x² - 3yx

Combine like terms and than subtract the coefficients of similar terms.

(5x² - 3x² + 4y² - 2y² - 3yx)

 = 2x² + 2y² -3xy

Example 4: Subtract y² + 3yx from x² + 4y².

Solution:

We have, (x² + 4y² ) - (y² + 3yx)

Change the sign of the term to be subtracted, we get

x² + 4y² - y² - 3yx

Combine like terms and than subtract the coefficients of similar terms.

= x² + 3y² - 3yx

Practice Questions on Subtraction of Algebraic Expression

Q1: Subtract y² + 5x² from 6x² + 2y²

Q2: A ribbon of length 8x² + 4y² is cut into two pieces. If length of one piece is 3x² + 3yx, find the length of the other piece.

Q3: Subtract yx² + 3xy² + 3yx from 7xy² + 8xy²

Q4: Find the third side of a triangle with perimeter 5yx + 20x² + 30y². If the other two sides of the triangle are 10x² + 4y² and 4x² + 2xy.

Q5: Subtract yx from 5xy + 4y²