Railways Notes / Mathematics (Quantitative Aptitude) / Chapter 19
Chapter 19 of 31

Algebra

Basic identities and linear equations — algebraic shortcuts that appear scattered across Age and Mixture problems too.

📖 ~4 min read 📐 RRB NTPC / Group D — Mathematics

Standard Identities

IdentityExpansion
(a+b)²a² + 2ab + b²
(a−b)²a² − 2ab + b²
a² − b²(a+b)(a−b)
(a+b)² − (a−b)²4ab
(a+b)² + (a−b)²2(a² + b²)

Solving Linear Equations

  • For two-variable equations, use substitution: isolate one variable from the simpler equation and plug into the other.
💡 Example: If a+b=12 and ab=32, find a²+b² → a²+b² = (a+b)²−2ab = 144−64 = 80 (no need to find a, b individually)

💡 Want More? Get the Full eBook

This free chapter covers the key concepts. For complete coverage with 500+ MCQs, mock tests, and previous year analysis — grab the premium eBook.

📚 Browse Premium eBooks →