Subtraction of Algebraic Expressions
2026-02-28 00:56 Diff
https://brightchamps.com/en-us/math/algebra/subtraction-of-algebraic-expressions

371 Learners

Last updated on October 30, 2025

The mathematical operation of finding the difference between two expressions is known as the subtraction of algebraic expressions. It helps simplify expressions and solve problems that involve constants, variables, and arithmetic operations.

What is Subtraction of Algebraic Expressions?

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

Subtracting algebraic expressions involves adding the additive inverse of the second expression to the first.

It requires changing the signs of the terms of the expression being subtracted and then combining the like terms. There are three components of an algebraic expression: 

Coefficients: These are constant values like -1, 4, etc. 

Variables: These are unknown quantities like x, y, z, etc. 

Operators: For subtraction, the operator is the minus (-) symbol.

How to do Subtraction of Algebraic Expressions?

When subtracting the algebraic expressions, students should follow the list of rules:

  1. Flip signs: Always flip the signs of each term of the second expression and perform addition. 
  2. Combine like terms: Only like terms can be subtracted from one another, so group all like terms together.
  3. Simplifying result: After all like terms are combined, there will be unlike terms remaining. Write the remaining unlike terms as they are, along with the like terms, to get the final result.

Methods to do Subtraction of Algebraic Expressions

The following are the methods of subtraction of algebraic expressions:

  • Horizontal Method
  • Column Method

Explore Our Programs

Horizontal Method

To apply the horizontal method for subtraction of algebraic expressions, use the following steps.

Step 1: Write both expressions in the same line using a minus sign in between.

Step 2: Remove the brackets and change the signs of the second expression.

Step 3: Combine the like terms.

Let’s apply these steps to an example:

Question: Subtract \((2x-y+4) from (5x+3y-2)\)

Step 1: Write both expressions in the same line, \((5x +3y-2)-(2x-y+4)\)

Step 2: Remove the brackets and change the signs of the second expression \(5x+3y-2-2x+y-4\)

5x and 2x are like terms having the same variable x, similarly, 3y and -y are also like terms.

Step 3: Write like terms together:\( (5x-2x)+(3y+y)+(-2-4)\)

Answer: \(3x+4y-6\)

Column Method

When subtracting the algebraic expressions using the column method, we write the expressions one below the other.

Make sure like terms are aligned in each column. Then change the signs of the second expression and add the expressions. 

For example, Subtract\( (2x-y+4) from (5x+3y-2)\)

Solution: Arrange the like terms vertically in columns

  5x   +  3y   -  2    ← Minuend (from which we subtract)
- 2x   -   y   +  4    ← Subtrahend (what we subtract)
-----------------------
  3x   + 4y   - 6

Therefore, upon subtracting \((2x-y+4) \)from \((5x+3y-2)\), we get \(3x   + 4y   - 6\)

Properties of Subtraction of Algebraic Expressions

In algebra, subtraction has some characteristic properties. These properties are listed below:

  • Subtraction is not commutative

    In subtraction, changing the order of the terms changes the result, i.e.,\( A - B ≠ B - A\)

  • Subtraction is not associative

    Unlike addition, we cannot regroup in subtraction. When three or more expressions are involved, changing the grouping changes the result.
    \((A − B) − C ≠ A − (B − C)\)

  • Subtraction is the addition of the opposite sign

    Subtracting an expression is the same as adding its opposite, so to make calculations easier, you can convert subtraction into addition by changing the signs of the second term.
    \(A − B = A + (−B)\)

  • Subtracting zero from an expression leaves the expression as is
    Subtracting zero from any expression results in the same algebraic expression: A - 0 = A

Tips and Tricks for Subtraction of Algebraic Expressions

Tips and tricks are useful for students to efficiently deal with the subtraction of algebraic expressions. Some helpful tips are listed below:

  • Always pay attention to signs before combining like terms.
  • If two expressions have identical terms, cross them out before starting the subtraction. This makes the expressions shorter and provides more clarity due to fewer terms.
  • Beginners and visual learners can benefit from using the box model or column method to avoid missing signs and mismatching terms.
  • Always enclose the second expression in brackets before changing signs. This helps prevent sign errors during subtraction.
  • After subtracting, add your result to the subtracted expression. If you get the original expression back, your subtraction is correct.

Common Mistakes and How to Avoid Them in Subtraction of Algebraic Expressions

Subtraction in algebra is comparatively more challenging than addition, often leading to common mistakes. However, being aware of these errors can help students avoid them.

Real-Life Application on Subtraction of Algebraic Expressions

Subtraction of algebraic expressions helps us find differences between quantities and make accurate comparisons. It is a key mathematical skill used to solve practical and technical problems in various fields.
 

  • Engineering: Engineers often subtract algebraic expressions to calculate the difference between designed and actual measurements.
  • Robotics: In robotics, subtraction helps determine the error between the desired and actual movements of a robot arm.
  • Architecture: Architects use subtraction of algebraic expressions to find remaining materials or design adjustments.
  • Physics: In physics, subtraction is used to calculate differences in speed, energy, or force.
  • Science Experiments: In labs, scientists subtract expressions to find differences in temperature or concentration levels between two samples.

Download Worksheets

Problem 1

Subtract 3x + 5 from 7x + 2

Okay, lets begin

4x - 3

Explanation

Use the horizontal method,

(7x + 2) - (3x + 5) 

= 7x + 2 - 3x - 5

= 4x - 3

Well explained 👍

Problem 2

Subtract 4a² − 3a + 2 from 7a² + a − 6

Okay, lets begin

3a2 + 4a - 8

Explanation

Use the horizontal method of subtraction

(7a2 + a − 6) - (4a2 − 3a + 2)

= 7a2 + a − 6 - 4a2 + 3a - 2

= 3a2 + 4a - 8

Well explained 👍

Problem 3

Subtract (2x − 3y) from (−x + 5y)

Okay, lets begin

-3x + 8y

Explanation

(−x + 5y) − (2x − 3y)

= −x + 5y − 2x + 3y

=  -3x + 8y

Well explained 👍

Problem 4

Subtract 3p² + 4pq − 5q²from 5p2 − 2pq + 3q²

Okay, lets begin

2p2−6pq+8q2

Explanation

5p2 − 2pq + 3q2 − (3p2 + 4pq − 5q2)

= 5p2 − 2pq + 3q2 − 3p2 − 4pq + 5q2

= 2p2−6pq+8q2

Well explained 👍

Problem 5

Subtract x²− 2xy + y² from 2x² + 3xy − y²

Okay, lets begin

x2 + 5xy − 2y2

Explanation

(2x2 + 3xy −y2) − (x2 − 2xy + y2)

= 2x2 + 3xy − y2 − x2 + 2xy − y2

= x2 + 5xy − 2y2

Well explained 👍

FAQs on Subtraction of Algebraic Expressions

1.Can we subtract unlike terms?

No, only like terms can be combined using subtraction; unlike terms are written as it is.

2.Is subtraction commutative in algebra?

No, the order of terms matters in subtraction; changing them changes the outcome.

3.What are the like terms?

Like terms have identical variables, including the exponents as well.

For example, 3x2 and 17x2 are like terms because both terms have the variable x raised to the power of 2.

4.What is the first step of the subtraction of algebraic expressions?

5.What method is used for the subtraction of algebraic expressions?

The horizontal method and the column method are used for subtracting algebraic expressions.

6.How can a parent help their child understand subtraction of algebraic expressions easily?

A parent can explain that subtracting algebraic expressions is like taking away one set of terms from another just as we subtract numbers, but with letters and signs.

7.How can a parent teach their child to identify like terms correctly?

A parent can sit with their child and color-code or underline terms with the same variables and powers. This helps the child visually connect and subtract like terms easily.

8.What can a parent do if their child mixes up addition and subtraction of expressions?

A parent can remind their child that addition keeps the signs the same, but subtraction means flipping all the signs of the second expression before combining.

9.What can a parent do if their child struggles to remember the subtraction steps?

Parents can create a simple checklist for their child: (1) Use brackets, (2) Change signs, (3) Combine like terms, (4) Simplify. Repetition builds memory and confidence.

Important Glossary for Subtraction of Algebraic Expressions

  • Algebraic expression: An algebraic expression is a combination of terms including variables, constants, and operators.
  • Like terms: Terms having the same variables raised to the same power are like terms.
  • Unlike terms: Terms having different variables or exponents, or both, are unlike terms.
  • Coefficient: The number in a term that multiplies a variable in an algebraic expression is a coefficient.
  • Simplification: When like terms are combined to reduce a longer expression, this process is known as simplification.

Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.