18 questions from actual SSC CPO papers · all shown free · click option to reveal solution
Algebraic identities are pre-proven mathematical formulas that help solve complex algebraic expressions quickly. These are your shortcuts to crack algebra problems in SSC CGL without lengthy calculations. Think of them as ready-made formulas that work every time.
Algebraic identities are universally true for all values of variables. They help expand, factorize, and simplify expressions. The most important ones follow specific patterns that SSC loves to test.
SSC CGL typically asks direct substitution problems, value finding questions, and simplification using identities. Common question types include finding the value of expressions like x² + 1/x² when x + 1/x is given, or simplifying complex algebraic fractions.
- The 'Recognition Method': Instead of expanding everything, learn to recognize patterns. If you see (something)² - (something else)², immediately think a² - b² = (a+b)(a-b). This saves 2-3 minutes per question.
Start with the given condition x + 1/x = 5
Square both sides: (x + 1/x)² = 5² = 25
Apply the identity (a + b)² = a² + 2ab + b² Here, a = x and b = 1/x
(x + 1/x)² = x² + 2(x)(1/x) + (1/x)²
25 = x² + 2(1) + 1/x²
25 = x² + 2 + 1/x²
x² + 1/x² = 25 - 2 = 23 Therefore, x² + 1/x² = 23.
Students often forget the middle term in expansions. In (a + b)², many write a² + b² and miss the 2ab term. Always count terms: square of binomial has THREE terms, cube has FOUR terms.
Also, students confuse signs in (a - b) expansions. Remember: alternate signs in (a - b)³.