Top 20 Algebra Formula For SSC Exams in 2025-26

Maths Wallah June 05, 2025

In this article we will know about Top 20 Algebra Formulas for SSC Exams, including identities, derivations (where needed), and use-cases that often appear in SSC CGL, CHSL, and other competitive exams.


🔢 Basic Algebraic Identities

1. (a + b)² = a² + 2ab + b²

  • Use: Expanding square of a sum.
  • Example: (3 + 5)² = 9 + 30 + 25 = 64

2. (a - b)² = a² - 2ab + b²

  • Use: Square of a difference.
  • Example: (6 - 2)² = 36 - 24 + 4 = 16

3. a² - b² = (a + b)(a - b)

  • Use: Factorization of difference of squares.
  • Example: 49 - 36 = (7 + 6)(7 - 6) = 13 × 1 = 13

4. (x + a)(x + b) = x² + (a + b)x + ab

  • Use: Expanding product of two binomials.
  • Example: (x + 2)(x + 3) = x² + 5x + 6

5. (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

  • Use: Expanding square of a trinomial.
  • Example: (1 + 2 + 3)² = 1 + 4 + 9 + 4 + 6 + 6 = 30

🧊 Cubic Identities

6. a³ + b³ = (a + b)(a² - ab + b²)

  • Use: Factorizing sum of cubes.
  • Example: 8 + 27 = (2 + 3)(4 - 6 + 9) = 5 × 7 = 35

7. a³ - b³ = (a - b)(a² + ab + b²)

  • Use: Factorizing difference of cubes.
  • Example: 27 - 8 = (3 - 2)(9 + 6 + 4) = 1 × 19 = 19

8. (a + b)³ = a³ + 3a²b + 3ab² + b³

  • Use: Expansion of cube of sum.
  • Example: (2 + 1)³ = 8 + 12 + 6 + 1 = 27

9. (a - b)³ = a³ - 3a²b + 3ab² - b³

  • Use: Expansion of cube of difference.
  • Example: (3 - 1)³ = 27 - 27 + 9 - 1 = 8

🔁 Special Expressions with Reciprocals

10. (x + 1/x)² = x² + 1/x² + 2

  • Use: If x + 1/x is known, find x² + 1/x².
  • Example: If x + 1/x = 3, then x² + 1/x² = 3² - 2 = 7

11. (x - 1/x)² = x² + 1/x² - 2

  • Use: Square of difference involving reciprocals.
  • Example: If x - 1/x = 5, then x² + 1/x² = 25 + 2 = 27

12. x³ + 1/x³ = (x + 1/x)³ - 3(x + 1/x)

  • Use: Derive cube expressions.
  • Example: If x + 1/x = 2, then x³ + 1/x³ = 8 - 6 = 2

13. x³ - 1/x³ = (x - 1/x)³ + 3(x - 1/x)

  • Use: Cube of difference of reciprocals.
  • Example: If x - 1/x = 3, then x³ - 1/x³ = 27 + 9 = 36

🧩 Factorization and Special Identities

14. a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)

  • Special Case: If a + b + c = 0, then
    a³ + b³ + c³ = 3abc
  • Use: Advanced questions in algebra or identities-based MCQs.

15. (a - b)⁴ + (b - c)⁴ + (c - a)⁴ ≥ 0

  • Use: Inequality questions in reasoning algebra.
  • Always non-negative since even powers are ≥ 0.

➗ Rational and Symmetric Expressions

16. (a² + b²)/(a + b) = a + b - (2ab)/(a + b)

  • Use: Simplify expressions involving sum of squares.
  • Example: If a = 2, b = 3 → (4 + 9)/(5) = 13/5 = 5 - (12/5)

17. If a + 1/a = x, then a² + 1/a² = x² - 2

  • Use: Convert between sum and square.
  • Example: If x = 4, then a² + 1/a² = 16 - 2 = 14

18. If a + 1/a = x, then a³ + 1/a³ = x³ - 3x

  • Use: Find cubes using linear values.
  • Example: If x = 3, then a³ + 1/a³ = 27 - 9 = 18

📈 Miscellaneous but Useful

19. (a² - b²)² = a⁴ - 2a²b² + b⁴

  • Use: Expansion of square of a difference of squares.
  • Can be used in algebraic simplifications.

20. If x + y + z = 0, then x² + y² + z² = 2(xy + yz + zx)

  • Use: Identity in questions with symmetric sums.
  • Helps in converting square terms to product terms.

🧠 Tips for SSC Exam Prep

  • Memorize the identities and practice how they are applied in different formats.
  • SSC often tricks candidates by combining 2–3 formulas.
  • Practice with previous year questions and mock tests.


Maths Wallah

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