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RRB Group D Algebraic Identities

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This page covers RRB Group D Algebraic Identities with complete concept notes, 3 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Algebraic Identities— Rules & Concept

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Core Concept

Read this first — the foundation of the topic

💡Key Rules and Properties

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

🔑Essential Formulas

• (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

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Exam Patterns

What 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. Shortcut Trick - 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.

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Worked Example

Solve this step-by-step before moving on

1

Step 1

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

2

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. Common Mistake: 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.

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Key Points to Remember

(a + b)² = a² + 2ab + b² - never forget the middle term 2ab
(a - b)² = a² - 2ab + b² - note the minus sign before 2ab
(a + b)(a - b) = a² - b² - difference of squares identity
a³ + b³ = (a + b)(a² - ab + b²) - sum of cubes factorization
a³ - b³ = (a - b)(a² + ab + b²) - difference of cubes factorization
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca - three variable expansion
When x + 1/x is given, find x² + 1/x² by squaring both sides
Recognize patterns first, then apply appropriate identity to save time

Exam-Specific Tips

(a + b)² has exactly 3 terms: a², 2ab, and b²
(a - b)³ = a³ - 3a²b + 3ab² - b³ with alternating signs
x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - yz - zx)
If a + b + c = 0, then a³ + b³ + c³ = 3abc
(a + b)³ - (a - b)³ = 2b(3a² + b²)
The coefficient of middle term in (a + b)² is always 2
a⁴ - b⁴ = (a² + b²)(a + b)(a - b)
(x + 1/x)² = x² + 1/x² + 2

Practice MCQs

Algebraic Identities — Practice Questions

3graded MCQs · easy to hard · full solution & trap analysis

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Practice 1easy

If x + y = 12 and xy = 35, find the value of x² + y².

Practice 2medium

If x + y = 12 and xy = 35, then find the value of x² + y².

Practice 3medium

If (a + b)² = 81 and (a − b)² = 25, find the value of ab.

60-Second Revision — Algebraic Identities

Remember: Square of binomial has 3 terms, cube has 4 terms
Formula: (a + b)(a - b) = a² - b² for quick factorization
Trap: Don't forget middle terms in expansions - very common error
Trick: If x + 1/x given, square it to find x² + 1/x²
Pattern: Recognize a² - b² form immediately for difference of squares
Sign Rule: (a - b)³ has alternating positive-negative signs
Quick Check: Count terms in your final answer to avoid missing any

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