Addition of Algebraic Expressions

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.

In this article, we will discuss Addition of Algebraic Expression and different rules and methods to perform addition of algebraic expressions.

What is 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.

What is 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:

• Constant
• Variable
• Coefficients
• Exponents

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.

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

Adding Algebraic Expressions FAQs

What are Algebraic Expressions?

Algebraic expressions are mathematical expressions containing variables, constants, and arithmetic operations.

What is Addition Rule for Algebraic Expressions?

The addition rule for algebraic expression is to combine like terms together and then add their coefficients.

What is Addition by Column Method in Algebraic Expression?

Column method for addition in algebraic expressions is a technique used to add algebraic expressions by organizing like terms vertically and then adding one column at a time.

How to Handle Negative Terms in Addition?

Negative terms are added or subtracted based on the sign rules of addition and subtraction.

What are Like Terms?

Like terms have the same variables raised to the same powers.

What is Order of Operations in Adding Algebraic Expressions?

Perform operations within parentheses first, then combine like terms.

How to Identify Unlike Terms?

Unlike terms have different variables or different powers of the same variables.

What is Difference Between Expressions and Equations?

Expressions represent quantities, while equations assert equality between expressions.

What is Addition and Subtraction in Algebra?

Addition and subtraction in algebra refers to the arithmetic operations used to solve algebraic expressions and equations in maths.