Algebraic Expressions - Class 7 Mathematics (CBSE)
Based on the 2025-26 NCERT syllabus for Class 7 Mathematics. This chapter introduces the formal language of algebra including terms, coefficients, operations on expressions, and evaluating expressions.
1. Why this chapter matters
Algebraic expressions are the language of mathematics. From simple formulas to complex equations, understanding how to manipulate expressions is essential. In CBSE exams, this chapter contributes 6-8 marks and is the foundation for Class 8 Factorisation and algebraic identities.
2. Variables and constants
Variable
A variable is a symbol (usually a letter) that can take different values. Examples: x, y, a, b, p, q.
Constant
A constant has a fixed value. Examples: 5, -3, 2/5, 0.7.
3. Terms of an algebraic expression
A term is a product of constants and variables separated by + or - signs.
Expression: 3x + 5y - 7z + 2 has four terms: 3x, 5y, -7z, 2.
Coefficient
The numerical factor of a term is called its coefficient.
- In 3x, coefficient of x is 3.
- In -7y, coefficient of y is -7.
- In z, coefficient of z is 1 (understood).
- In -xy, coefficient of xy is -1.
Factors of a term
Each term is a product of its factors. Term 5xy has factors: 5, x, and y.
4. Like and unlike terms
Like terms
Terms having the same variable factors (same variables with same exponents). Example: 3x and -7x are like terms. 4xy and 9xy are like terms.
Unlike terms
Terms with different variable factors. Example: 3x and 4y are unlike. 5x and 5x-squared are unlike.
Why it matters
Only like terms can be added or subtracted.
5. Types of algebraic expressions
| Type | Definition | Example |
|---|---|---|
| Monomial | One term | 5x, -3y, 7 |
| Binomial | Two terms | 2x + 3, 5a - 4b |
| Trinomial | Three terms | x + y + z, a - 2b + 3c |
| Polynomial | One or more terms | Any of the above |
6. Addition and subtraction of expressions
Adding algebraic expressions
Add the coefficients of like terms. Keep unlike terms as they are.
(3x + 5y - 2) + (7x - 3y + 8) = (3x + 7x) + (5y - 3y) + (-2 + 8) = 10x + 2y + 6
Subtracting algebraic expressions
Subtract the coefficients of like terms.
(8x + 3y - 5) - (3x - 2y + 7) = 8x + 3y - 5 - 3x + 2y - 7 = (8x - 3x) + (3y + 2y) + (-5 - 7) = 5x + 5y - 12
Important rule
When subtracting, change the sign of each term of the expression being subtracted, then add.
7. Finding the value of an expression
To find the value of an expression, substitute the given values for the variables, then simplify using BODMAS.
Example: Evaluate 3x + 5y - 2 when x = 2 and y = -1.
3(2) + 5(-1) - 2 = 6 - 5 - 2 = -1.
Example: Evaluate a-squared + 2ab + b-squared when a = 3 and b = -2.
(3)squared + 2(3)(-2) + (-2)squared = 9 - 12 + 4 = 1.
8. Worked examples
Example 1: Identify the terms and coefficients in 2x-squared - 3xy + 7y - 5.
| Term | Coefficient | Variable part |
|---|---|---|
| 2x-squared | 2 | x-squared |
| -3xy | -3 | xy |
| 7y | 7 | y |
| -5 | -5 | (constant) |
Example 2: Add 4a - 3b + 7 and -2a + 5b - 3.
(4a - 2a) + (-3b + 5b) + (7 - 3) = 2a + 2b + 4.
Example 3: Subtract 2x - 4y + 5 from 7x - y - 3.
(7x - y - 3) - (2x - 4y + 5) = 7x - y - 3 - 2x + 4y - 5 = (7x - 2x) + (-y + 4y) + (-3 - 5) = 5x + 3y - 8.
Example 4: Find the value of 2x-squared - 3x + 5 when x = -2.
2(-2)squared - 3(-2) + 5 = 2(4) + 6 + 5 = 8 + 6 + 5 = 19.
9. Common mistakes and how to fix them
| Mistake | Fix |
|---|---|
| Adding unlike terms (e.g., 3x + 2y = 5xy) | Only add coefficients of LIKE terms |
| Forgetting sign change during subtraction | Change every sign in the subtracted expression |
| Confusing term and coefficient | Coefficient is the number multiplied by the variable part |
| Considering 5x and 5x-squared as like | They have different exponents; they are unlike |
| Substituting without brackets | Use brackets when substituting negative values |
10. CBSE exam focus
| Question type | Marks | Frequency |
|---|---|---|
| Identify terms and coefficients | 2 marks | 1 question |
| Like/unlike terms identification | 2 marks | 1 question |
| Addition of expressions | 2-3 marks | 1 question |
| Subtraction of expressions | 2-3 marks | 1 question |
| Find value of expression | 3 marks | 1 question |
11. Self-test
- Write the terms and coefficients of: 3x-squared - 5xy + 2y - 8.
- Add: (5m - 3n + 2) + (-2m + 7n - 5).
- Subtract: (9p - 4q + 6) - (3p + 2q - 5).
- Find the value of 2a + 3b - 4c when a = 5, b = -2, c = 1.
- Evaluate: x-squared - 3x + 2 when x = -1.
- Simplify: (3x + 2y - z) - (5x - 3y + 2z) + (x + y + z).
12. Answer key
- Terms: 3x-squared (coeff 3), -5xy (coeff -5), 2y (coeff 2), -8 (constant).
- (5m - 2m) + (-3n + 7n) + (2 - 5) = 3m + 4n - 3.
- 9p - 4q + 6 - 3p - 2q + 5 = (9p - 3p) + (-4q - 2q) + (6 + 5) = 6p - 6q + 11.
- 2(5) + 3(-2) - 4(1) = 10 - 6 - 4 = 0.
- (-1)squared - 3(-1) + 2 = 1 + 3 + 2 = 6.
- 3x + 2y - z - 5x + 3y - 2z + x + y + z = (3x - 5x + x) + (2y + 3y + y) + (-z - 2z + z) = -x + 6y - 2z.
13. Quick revision
- Term = constant x (product of variables).
- Coefficient = the numerical factor of a term.
- Like terms have identical variable parts.
- Only like terms can be added or subtracted.
- Subtraction: change all signs of the subtracted expression.
- To find value, substitute and apply BODMAS.
- Monomial = 1 term, binomial = 2 terms, trinomial = 3 terms.
