Subtraction of Algebraic Expressions
Subtraction of algebraic expression is almost similar to subtracting numbers and finding their difference but in the case of algebraic expressions, like terms and the unlike terms are sorted together to solve the algebraic expressions problems, and then operations are performed..
In this lesson, let's learn the subtraction of algebraic expressions, rules, and methods to subtract algebraic expressions with solved examples.
What is Subtraction of Algebraic Expressions?
For subtracting two or more algebraic expressions, it requires categorizing the terms in an algebraic expression into two types  like and unlike terms. Then, taking up the like terms and then subtracting them accordingly. The other way is to follow the horizontal method that requires writing the expressions to be subtracted below the expression from which it is to be subtracted. Like terms are placed below each other. The sign of each term that is to be subtracted is reversed and then the resulting expression is added normally.
An algebraic expression (or) a variable expression is a combination of terms by operations such as addition, subtraction, multiplication, division, etc. An example of an algebraic expression is 5x+7. We can categorize the terms in an algebraic expression into two types  like and unlike terms.
 Terms containing the same variable raised to the same power are known as like terms. In like terms, one can only change the numerical coefficient. Examples of like terms are 5x and 13x, 7y^{3} and 3y^{3}, a^{4} and 6a^{4}
 Terms that have different variables or the same variable raised to different powers are known as, unlike terms. Examples of unlike terms are 5x and 5y, 2m^{5} and 8m^{3}, 56p^{3 }and q^{3}
How to Subtract Algebraic Expressions?
Can we subtract 3 apples from 4 bananas? The answer is NO. We cannot subtract 3 apples from 4 bananas, as they are two different objects. Similarly, in the case of terms in an algebraic expression, we cannot subtract two or more unlike terms. An important point to remember while subtracting algebraic expressions is that we can only subtract like terms. There are two methods to do subtraction of algebraic expressions  the horizontal method and the column method.
Horizontal Method
Steps to be followed while doing algebraic expression subtraction by the horizontal method is written below:
 Step 1: Write all the expressions in a horizontal line by putting them into brackets and put subtraction signs in between.
 Step 2: Group all the like terms together from all the expressions and rewrite it in a single expression.
 Step 3: Add numerical coefficients of all the like terms followed by the common variable.
 Step 4: Rewrite the simplified expression, and make sure all the terms in the final answer are unlike terms.
Column Method
Steps to be followed to do subtraction of algebraic expressions by column method is written below:
 Step 1: Write both expressions one below the other. Make sure you have written like terms in one column. If there is a term whose like term is not there in the second expression, for example, 2x^{2}, then either write below it or leave that column blank.
 Step 2: Change the operators in the last row (second expression), for example, (+) to () and () to (+).
 Step 3: Consider the changed signs and add the numerical coefficient of each column (like terms) and write below it in the same column followed by the common variable.
Related Topics
 Addition of Algebraic Expressions
 Multiplication of Algebraic Expressions
 Division of Algebraic Expressions
 Factorization of Algebraic Expressions
 Combining Like Terms Calculator
Important Notes
 Subtraction of algebraic expressions can be done by two methods: the horizontal method and the column method.
 It is always better to subtract two expressions at one time. Never try to subtract three or more expressions together through the column method.
 Operators inside the brackets need to be changed if there is a negative sign outside the brackets.
 If there is no sign written with the first term of the algebraic expression, we consider it as positive. For example, 3x is the same as +3x.
Examples on Subtraction of Algebraic Expressions

Example 1: Determine the length of the third side of the triangle whose perimeter is 4x^{2}+17xy+5 units and the length of the other two sides are 5xy3x^{2} and x^{2}+5xy2.
Solution:
Given: Perimeter of the triangle= 4x^{2}+17xy+5 units, other two sides = 5xy3x^{2} and x^{2}+5xy2
We know that the perimeter of a triangle is the sum of all its sides. So, to find the length of side AC, we need to add the length of the other two sides and subtract that from the perimeter.
Sum of the other two sides can be calculated as,
(x^{2}+5xy2)+(5xy3x^{2})
= x^{2}3x^{2}+5xy+5xy2
= 2x^{2}+10xy2
Now, we subtract it from the perimeter of the triangle,
(4x^{2}+17xy+5)(2x^{2}+10xy2)
=4x^{2}+17xy+5+2x^{2}10xy+2
=4x^{2}+2x^{2}+17xy10xy+5+2
=6x^{2}+7xy+7
Therefore, the length of the third side is 6x^{2}+7xy+7 units.

Example 2: A metal rod of length (5mn2n+1) units is cut into two parts. If the length of the bigger part is (3mn+n) units, find the length of the smaller part of the rod.
Solution:
Given: Total length of rod = (5mn2n+1) units, the length of the bigger part of the rod = (3mn+n) units
To find the length of the smaller part of the rod, we need to subtract the length of the larger part from the total length of the rod.
Therefore, the length of the smaller part of the rod is (2mn3n+1) units.
FAQs on Subtraction of Algebraic Expressions
What Is Subtraction of Algebraic Expressions in Math?
Subtraction of algebraic expressions requires categorizing the terms in an algebraic expression into like and unlike terms. Then we group together all like terms such that the simplified expression will only have unlike terms in it.
What Is the Rule for Adding and Subtracting Algebraic Terms?
The basic rule for adding or subtracting algebraic terms is to add or subtract only like terms. Also, in the case of subtraction, if there is a negative sign outside the bracket, then we change the operators of the terms inside the bracket and then solve further.
Do You Add or Subtract Like Terms To Solve the Algebraic Expressions?
Yes, we can add or subtract only like terms by adding/subtracting their numerical coefficients.
How To Solve Addition and Subtraction of Rational Algebraic Expressions?
For addition or subtraction of two rational expressions with the same denominator:
 Step 1: Add or subtract the numerators.
 Step 2: Write the result so obtained over the common denominator.
In case, the denominators are not the same, make them the same by manipulating them. In other words, in order to get a common denominator.
How To Add or Subtract Algebraic Expressions with Exponents?
There is a simple rule to add or subtract algebraic expressions with exponents. For example, 5x^{3}+8x^{3}=13x^{3}
Both the variables and the exponents of the variables must be the same so that you just need to perform the required operations on the coefficients only, as we can combine if they have exactly the same variables with exactly the same powers.
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