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IBPS PO Algebraic Identities

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This page covers IBPS PO Algebraic Identities with complete concept notes, 1 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Algebraic Identities— Rules & Concept

Core ConceptRead this first — the foundation of the topic

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.

Key RulesCore rules you must know cold

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.

Formula BlockMemorise — at least one formula appears in every paper

• (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

• (a - b)³ = a³ - 3a²b + 3ab² - b³

• a³ + b³ = (a + b)(a² - ab + b²)

• a³ - b³ = (a - b)(a² + ab + b²)

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

Exam PatternsWhat examiners ask — read before attempting PYQs

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.

ShortcutsUse these to save 30–60 seconds per question

- 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.

Worked ExampleSolve this step-by-step before moving on

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Step 1

Start with the given condition x + 1/x = 5

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Step 2

Square both sides: (x + 1/x)² = 5² = 25

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Step 3

Apply the identity (a + b)² = a² + 2ab + b² Here, a = x and b = 1/x

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Step 4

(x + 1/x)² = x² + 2(x)(1/x) + (1/x)²

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Step 5

25 = x² + 2(1) + 1/x²

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Step 6

25 = x² + 2 + 1/x²

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Step 7

x² + 1/x² = 25 - 2 = 23 Therefore, x² + 1/x² = 23.

Exam TrapsCommon mistakes students make — avoid these

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.