Addition of Algebraic Expressions
Last Updated :
23 Jul, 2025
Algebraic expressions are mathematical phrases that can include numbers, variables, and operation symbols. The addition of algebraic expressions involves combining like terms to simplify the expression.
Addition of Algebraic Expression involves combining like terms of the given expression and then adding their numeral coefficients. We can add two or more algebraic expressions together. Adding algebraic expressions is a widely used concept in problem-solving.
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In this article, we will discuss Addition of Algebraic Expression and different rules and methods to perform addition of algebraic expressions.
Algebraic Expression
Algebraic expression is a combination of terms containing constants and variables, which are combined by mathematical operations. They are the building blocks of equations and inequalities, representing unknown quantities (variables) and known values (constants) with various mathematical operations.
Algebraic Expressions serve as a representation of a quantity or value that can change depending on the values assigned to the variables. For example, 3x + 5y is an algebraic expression, where x and y are variables(changing value), and 3 and 5 are constants.
Addition of Algebraic Expression
Addition of algebraic expressions is similar to the addition of numbers. In algebraic expression we need to combine the like terms first to simplify the expression or to solve equations. When adding algebraic expressions, we simply add the coefficients of like terms while keeping the variables unchanged. Steps for addition of algebraic expressions involve:
- Combining like terms, which are terms that have the same variables raised to the same powers.
- Adding numeral coefficients of like terms.
Addition of algebraic expressions involves finding the sum of two or more expressions. For example, when adding 3x + 2y and 5x + 3y, you add the coefficients of x and y separately to get the result 8x + 5y.
How to do Addition of Algebraic Expression?
Addition of algebraic expressions, focuses on combining like terms and simplifying the resulting expression. Here's a step-by-step guide for adding algebraic expressions:
- Identify Like Terms: Find all the terms with identical variables and exponents. For Example: (2x2, 4x2) , (5x, -7x) and (3, 1) are pairs of like terms in the expression (2x2 + 5x +3) + (4x2 - 7x + 1).
- Group like Terms together: Arrange the expression, placing like terms in close proximity. For Example: (2x2 + 4x2) + (5x - 7x) + (3 + 1).
- Combine like terms by adding their coefficients: Perform the addition within each group while maintaining the variables and exponents. Example: 6x2 - 2x + 4.
- Simplify 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.
Rules for Addition of Algebraic Expression
- Combine like terms by adding their coefficients.
- Keep the variables unchanged while performing addition.
- Arrange the terms in the resulting expression in standard form.
Algebraic Expression Addition Method
Addition of Algebraic Expression can be done by two methods namely:
- Horizontal Method
- Column Method
Step-by-step explanations and examples of each method is given below:
Horizontal Method
Follow the below given steps to add algebraic expressions by horizontal method:
- Identify like terms: Arrange the expressions side-by-side, ensuring terms with the same variables and exponents are aligned horizontally.
- Combine like terms: Add the coefficients of each group of like terms. Remember to keep the variable part and exponent the same. For example, 2x + 5x becomes 7x.
- Write the simplified expression: Combine all the simplified terms and collect the remaining terms into a single expression.
In the horizontal method, terms with the same variables are aligned and added accordingly. An example of addition of algebraic expression by horizontal method is given below:
Example: Add 3x2 + 2x - 5 and 5x2 - 4x + 1
Solution:
We have (3x2 + 2x - 5) + (5x2 - 4x + 1)
Step 1: Identify like terms
(3x2 + 5x2) + (2x – 4x) + (-5 + 1)
Step 2: Combine like terms
(8x2) + (– 2x) + (-4)
Step 3: Write the simplified expression
8x2 – 2x - 4
Column Method
To add algebraic expressions by column method follow the below given steps:
- Arrange expressions vertically: Write each expression one below the other, aligning terms with the same variable and exponent in the same columns. Add extra rows of zeros if needed to make all columns equal in length.
- Add coefficients: In each column, add the corresponding coefficients. If a column only has one term, simply write that term in the result row.
- Write the simplified expression: Combine all the terms in the result row. Similar to the horizontal method.
The column method involves writing the expressions vertically and adding corresponding terms. An example of addition of algebraic expression by column method is given below:
Example: Add 2x2 + 3xy - 1 and 4x2 - 2xy + 5
Solution:
Components of Algebraic Expressions
The components of algebraic expressions include:
Constants
Constants are fixed values. These are fixed numerical values that do not change.
Examples of constants include numbers like 2, 5 and π.
Variables
Variables are symbols. These are symbols that are used to represent unknown or varying quantities.
Example: Some of the commonly used variables include x, y, and z.
Coefficients
Coefficients are multipliers of variables. These are the numerical factors that accompany variables.
Example: In the expression 33x, 33 is the coefficient of x.
Exponents
Exponents are powers. These represent the number of times a variable is multiplied by itself.
For instance, in the term 2x3, the exponent of x is 3.
Also Read
Addition of Algebraic Expression Examples
Example 1: Simplify and perform addition of below expression: (3x + 2y) + (5x - 3y)
Solution:
We have (3x + 2y) + (5x - 3y)
Combine and group like terms together
(3x + 5x) + (2y - 3y)
Perform operations within parentheses first.
(8x) + (-y)
Simplify the expression
8x - y
Example 2: Find the sum of the given expression : 2a2b - 3ab2 + 4a2b + 5ab2.
Solution:
We have 2a2b - 3ab2 + 4a2b + 5ab2
Combine and group like terms
(2a2b + 4a2b) + (- 3ab2 + 5ab2)
Perform operations within parentheses first.
(6a2b) + (2ab2 )
Simplify the expression
6a2b + 2ab2
Example 3: Simplify and perform addition of the given expression: 7p2q - 2pq2 + 3p2q - 4pq2
Solution:
Combine like terms by adding or subtracting their coefficients.
7p2q + 3p2q - 2pq2 - 4pq2
Keep similar terms together while adding.
Perform operations within parentheses first.
= (7p2q + 3p2q )+ (- 2pq2 - 4pq2)
= 10p2q - 6pq2
Example 4: Add the following algebraic expressions: x2 + 2xy + y2 + 3xy - 4x2 - 2y2
Solution:
Combine like terms by adding or subtracting their coefficients.
=x2 - 4x2 + 2xy + 3xy + y2 - 2y2
Keep similar terms together while adding.
Perform operations within parentheses first.
= (x2 - 4x2) + (2xy + 3xy) + (y2 - 2y2)
= -3x2 + 5xy - y2
Addition of Algebraic Expressions Practice Questions
Q1: Perform the addition: 2x2 + 3xy - 4x2 - 2xy
Q2: Add the following algebraic expressions: 5a2b - 2ab2 + 3a2b - 4ab2
Q3: Simplify: 3pq - 2qr + 5pq - 3qr
Q4: Find the sum: x3 + 2x2y - xy2 + 3x3 - 2x2y - xy2
Q5: Add: 2a2b + 4ab2 - 3a2b + 5ab2
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