Class 7 - Addition and Subtraction of Algebraic Expressions: Concepts and Solved Examples

Addition and subtraction of algebraic expressions are important concepts in Class 7 maths that help students simplify and solve expressions involving variables and constants. These operations are based on combining like terms, which means terms that have the same variables raised to the same powers. In this guide, you will learn how to perform addition and subtraction of algebraic expressions step by step. You will also understand the rules for combining like terms and see examples that make the concept easier to grasp.

Table of Contents

• What are Algebraic Expressions?
• Addition and Subtraction of Algebraic Expressions
• Addition of Algebraic Expressions
• Subtraction of Algebraic Expressions
• Solved Examples on Addition and Subtraction of Algebraic Expressions
• Practice Questions on Addition and Subtraction of Algebraic Expressions

What are Algebraic Expressions?

An algebraic expression is a combination of variables, constants (fixed numbers), and arithmetic operations. It represents a value that can change depending on what the variable equals.

Examples: 3x + 5,  2y − 7, 4a² + 3b − 9,  x² + 2xy + y², 5p − 2q + 3r

Given below is a diagrammatic method of representing terms and factors of an algebraic expression.

An algebraic expression does not have an equals sign (=). As soon as you add an equals sign, it becomes an equation. An expression simply represents a mathematical quantity.

Addition and Subtraction of Algebraic Expressions

When adding or subtracting algebraic expressions, the first step is to group the terms into like terms and unlike terms. Once identified, only the like terms can be combined to simplify the expression.

Like terms have the same variables raised to the same powers, so they can be added or subtracted easily. On the other hand, unlike terms have different variables or exponents, which means they cannot be combined.

Addition of Algebraic Expressions

An algebraic expression may consist of like and unlike terms. When adding algebraic expressions, group the like terms and add. The sum of two or more like terms is a like term whose numerical coefficient is the sum of the numerical coefficients of all the like terms. 

There are two standard methods, the horizontal method (working across) and the column method (working downward, like in long addition). Both give the same answer.

Horizontal Method

In the horizontal method, you write all expressions on one line, open the brackets, group the like terms together, and then add their coefficients.

1. Write all expressions separated by the addition (+) symbol, each in its own bracket.

2. Open all brackets. Since we are adding, the signs inside stay the same.

3. Identify and group all like terms.

4. Add the coefficients of each group of like terms. Write the variable part unchanged.

5. Write the final simplified expression by joining all the results.

Column Method

In the column method, you stack the expressions on top of each other, aligning like terms in the same column, and then add downward, just like long addition with regular numbers. This method is especially helpful with longer expressions because it reduces the chance of missing or misplacing terms.

Example: Add 4x² + xy – 6 and 6x² + 8xy.

Horizontal method:

 (4x² + xy – 6) + (6x² + 8xy)

= 4x² + xy – 6 + 6x² + 8xy (Combine the like terms.)

= 4x² + 6x² + xy + 8xy – 6

= 10x²  + 9xy – 6

Column method: Arrange the like terms column-wise and add.
 4x2+xy−6+6x2+8xy10x2+9xy−6

Subtraction of Algebraic Expressions

When subtracting algebraic expressions, we subtract a like term from a like term.

The difference of two like terms is a like term whose numerical coefficient is the difference of the numerical coefficients of the like terms.

The core rule is that when you subtract an expression, you change the sign of every single term inside the bracket being subtracted. Positive terms become negative, and negative terms become positive.

Horizontal method

1. Write the expressions with the subtraction (−) symbol between them.

2. Open the brackets. For the expression being subtracted, reverse the sign of every term inside it.

3. Group like terms together from all the terms now written out.

4. Subtract the coefficients of each group of like terms.

5. Write the final simplified expression.

Column method

1. Arrange the given expressions in rows such that the like terms are one below the other.

2. The expression to be subtracted should be in the second row.

3.  Inverse the sign of each term in the second row.

4. Now, simplify the like terms column-wise.

Example: Subtract 7x – 6y + 2z from 4z – 3y + 9x.

Horizontal method:

4z – 3y + 9x – (7x – 6y + 2z). (Put the expression in brackets with a minus outside the brackets.)

= 4z – 3y + 9x – 7x + 6y – 2z (Inverse the sign of each term inside the bracket.)

= 4z – 2z – 3y + 6y + 9x – 7x (Combine the like terms and simplify.)

= 2z + 3y + 2x = 2x + 3y + 2z

Column method:

9x−3y+4z−7x+6y−2z2x+3y+2z

Solved Examples on Addition and Subtraction of Algebraic Expressions 

Example 1: Find the sum of 15a + 11b – 13c – 17, 3a – 4b – cand a – b + 2c + 3.

Solution: (15a + 11b – 13c – 17) + (3a – 4b – c) + (a – b + 2c + 3)

= 15a + 3a + a + 11b – 4b – b – 13c – c + 2c – 17 + 3

= 19a + 6b – 12c – 14

Example 2: Find the sum of 6x + 7y + 8z, 7z – 11y – 9z and 8y – z using the column method.

Solution:  6x+7y+8z−11y+7z−9z+8y−z6x+4y+5z

Therefore, (6x + 7y + 8z) + (7z – 11y – 9z) + (8y – z ) = 6x + 4y + 5z.

Example 3: Subtract 3a² + 7a – 3 from 5a² – 5a – 8 using the column method.

Solution:  5a2−5a−8−3a2−7a+32a2−12a−5

(5a² – 5a – 8) - (3a² + 7a – 3) = 2a² – 12a – 5.

Example 4: Subtract x³ – 5yz + y³ from –9yz – 2x³ - 5y³

Solution:  (−9yz−2x3−5y3)−(x3−5yz+y3)=−9yz−2x3−5y3−x3+5yz−y3

= (−2x³ − x³) + (−9yz + 5yz) + (−5y³ − y³) = −3x³ − 4yz − 6y³ = −3x³ − 4yz − 6y³ 

=  −3x3−4yz−6y3.

Example 5: What must be added to 4a³ – 7a – a² + 11 to get a – a³ – 2a² – 9?

Solution: We are given (4a³ - 7a - a² + 11) + X = a - a³ - 2a² - 9

X=a−a3−2a2−9−4a3+7a+a2−11

−a3−2a2+a−9−4a3+a2+7a−11−5a3−a2+8a−20

Practice Questions on Addition and Subtraction of Algebraic Expressions

1. Subtract: (10x − 8y + 12) and (−2x + 3y + 2) from (4x + 6y − 5)

2. Add: (4x + 6y − 5) + (10x − 8y + 12) + (−2x + 3y + 2)

3. Add: (4x + 3) + (8x + 9) + (−6x − 5)

4. Add: (4x² + 5x + 6) and (x² + 10x − 8) and (−2x² − 2x + 3)

5. Add: (4x + 6y − 5) and (10x − 8y + 12) and (−2x + 3y + 2)

6. Subtract (3p² − 5p + 2) from (7p² + 2p − 4)

7. What should be added to (3x² − 5x + 2) to get (5x² + 2x − 1)?

8. Simplify: (6x² + 3x − 1) + (2x² − 7x + 4) − (x² + x − 5)

9. What should be subtracted from (4a − 3b + 2c) to get (a + b − c)?

10. A triangle has sides of length (2x + 3), (4x − 1), and (x + 5). Find its perimeter.