Algebra & Geometry
Syllabus Unit: Quantitative Aptitude
Why it matters
Chapter overview
This topic pairs the fixed set of algebraic identities used for instant factorisation and simplification with the classical geometry — lines, angles, triangles, circles and mensuration — that SSC CGL tests as direct formula-application MCQs. Together they cover roughly a quarter of the Quantitative Aptitude section, rewarding memorised identities and theorems over derivation from scratch.
1Algebraic Identities & Factorisation
A fixed set of identities — (a+b)², a²−b², a³+b³, and a handful more — turns messy factorisation into fast pattern matching.
Learning Objectives
- Apply (a+b)² = a²+2ab+b², (a−b)² = a²−2ab+b², and a²−b² = (a+b)(a−b) to factorise or simplify expressions.
- Apply the cube identities a³+b³ = (a+b)(a²−ab+b²) and a³−b³ = (a−b)(a²+ab+b²).
- Factorise a quadratic trinomial ax²+bx+c by splitting the middle term into two factors of ac summing to b.
- Apply a³+b³+c³−3abc = (a+b+c)(a²+b²+c²−ab−bc−ca) to three-variable expressions, including the special case where a+b+c=0.
Key Terms
Nearly every 'simplify' or 'factorise' question in SSC algebra is a direct match to one of a small set of memorised identities — recognising the pattern is faster than expanding and solving from scratch.
Worked example: splitting the middle term
x²−5x+6: find two numbers multiplying to +6 and adding to −5 → −2 and −3. So x²−5x+6 = (x−2)(x−3).