Algebra for Competitive Exams: From Basics to Advanced

Algebra is essential for SSC CGL (5-6 questions) and useful in banking too. Master these concepts systematically.

Essential Identities (Must Memorize)

(a+b)² = a² + 2ab + b². (a-b)² = a² - 2ab + b². (a+b)(a-b) = a² - b². (a+b)³ = a³ + 3a²b + 3ab² + b³. a³ + b³ = (a+b)(a² - ab + b²). a³ - b³ = (a-b)(a² + ab + b²).

If a + 1/a = k Type Questions

If a + 1/a = k, then: a² + 1/a² = k² - 2. a³ + 1/a³ = k³ - 3k. a⁴ + 1/a⁴ = (a² + 1/a²)² - 2. These formulas solve 80% of SSC algebra questions.

Factorization Tricks

For x² + bx + c: Find two numbers whose sum = b and product = c. For expressions with symmetric variables: Use factor theorem — if putting a=b makes expression 0, then (a-b) is a factor.