Subtraction of Algebraic Expressions (original) (raw)
Last Updated : 23 Jul, 2025
**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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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 3x 2 + 2x - 5 from 5x 2 - 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 (2a 2 + 3b) - (a 2 - 2b).
**Solution:
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: 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 2x 2 + 5x from 4x 2 - 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 6x 2 + 12x by 3x.
Given,(6x2 + 12x ) ÷ 3x
(6x2 ÷ 3x) + (12x ÷ 3x)
= 2x + 4
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Examples of Subtraction of Algebraic Expression
**Example 1: Subtract 3x 2 + 2x from 4x 2 + 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+ 3y 2 + 4x 2 . 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 2y 2 + 3x 2 + 3yx from 5x 2 + 4y 2
**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 y 2 + 3yx from x 2 + 4y 2 .
**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 y 2 + 5x 2 from 6x 2 + 2y 2
**Q2: A ribbon of length 8x 2 + 4y 2 is cut into two pieces. If length of one piece is 3x 2 + 3yx, find the length of the other piece.
**Q3: Subtract yx 2 + 3xy 2 + 3yx from 7xy 2 + 8xy 2
**Q4: Find the third side of a triangle with perimeter 5yx + 20x 2 + 30y 2 . If the other two sides of the triangle are 10x 2 + 4y 2 **and 4x 2 + 2xy.
**Q5: Subtract yx from 5xy + 4y 2