In competitive exams like SSC, Banking, and Railways, Algebraic Identities play a crucial role in the Quantitative Aptitude section. These identities are powerful tools that help in simplifying complex algebraic expressions quickly, avoiding lengthy calculations. Whether it’s a simplification-based question or one hidden inside a tricky expression, knowing these identities gives you a significant speed advantage.
In this blog, we will provide all the details about the Algebraic Identities for exams in 2024–25 including definitions, short notes, formulas, tricks, solved questions, common mistakes, and more.
What Are Algebraic Identities in Quantitative Aptitude?
Algebraic Identities are equations that hold true for all values of variables involved. These identities simplify complex algebraic expressions and help solve problems without full expansion or lengthy calculation.
This topic frequently appears in competitive exams because it tests the candidate’s ability to apply basic algebraic principles to solve expressions quickly and accurately.
Skills Required:
- Formula memorization
- Speed-based mental calculations
- Pattern recognition
- Simplification logic
Why Is Algebraic Identities Important in Competitive Exams?
Algebraic identities form the foundation of many Quantitative Aptitude questions, especially in topics like simplification, factorization, quadratic equations, and number systems.
| Exam | No. of Questions | Difficulty |
| SSC CGL / CHSL | 1–2 | Easy |
| IBPS PO / SBI PO | 1–2 | Moderate |
| RRB NTPC / Group D | 1 | Easy |
| State PSC / Police | 1–2 | Moderate |
Algebraic Identities Quantitative Aptitude Short Notes
Some of the commonly used identities while solving algebra problems are as follows:
Concepts Used in Algebraic Identities Questions
Some of the commonly used concepts in algebraic identities are as follows:
What Are the Types of Algebraic Identities Questions in Quantitative Aptitude?
Different question types based on algebraic identities include:
- Direct: Simplify using direct application of identity
- Puzzle-based: Hidden values or variables needing indirect use of identity
- Coded: Identities applied in numerical coding problems
- Mixed-concept: Combined with surds, equations, or simplifications
Algebraic Identities Formulas for Quantitative Aptitude
Memorizing and practicing these formulas can help you save time:
Use pattern-matching to directly apply them instead of full expansion.
Algebraic Identities Tricks for SSC CGL and Other Exams
Some of the quick strategies to solve identity-based problems faster:
- Identify the structure: Match question with standard form
- Avoid expansion: Use identities, don’t manually multiply
- Use substitution: Assign values like a=2, b=1if options are value-based
- Compare options: Eliminate wrong expressions via reverse checking
- Recognize cube and square forms immediately in expressions
- Break large expressions into smaller identity chunks
Solved Algebraic Identities Questions from 2024–25 Exams
Memory-based and mock-based solved questions are as follows:
SSC CGL 2024 Tier 1 – Shift 2 (Memory-Based)
IBPS PO Prelims 2024 – Mock Test
RRB NTPC 2024 CBT 1 (Based on memory)
Algebraic Identities Concepts for Bank Exams
Bank exams like IBPS PO and SBI PO frequently include twist-based identity questions.
Example:
Common Mistakes to Avoid while Solving Algebraic Identities
While solving Algebraic Identities Quantitative Aptitude questions, candidates must keep the below details in mind:
- Forgetting signs: Misplacing ‘+’ or ‘−’ leads to incorrect simplification.
- Expanding instead of using identity: Wastes time and increases error chances.
- Wrong identity matching: Misapplying cube for square identities.
- Calculation errors: Skipping steps or missing multiplication leads to wrong answers.
- Confusing a^2 – b^2 with (a-b)^2: Remember the formulas distinctly.
What Are Related Topics I Should Revise Next?
Topics you should revise next are as follows:
- Questions based on Time and Distance
- Rules and Practice Questions of Simplification
- Shortcuts and Patterns of Number Series
- Various types of Questions Based on Data Interpretation
- Tricks & Examples of Inequalities
FAQs
Identities always hold true, while expressions need evaluation and may not be equal.
They simplify complex expressions and save time during problem-solving.
Simplification, factorization, and expression comparison are common types.
You should remember the most common ones the rest can be derived with practice.
Trying to expand or solve without recognizing that an identity can simplify it.
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