Algebraic Identities Formulas, Concepts, Tricks and Tips

Published on 6 August 2025 by

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
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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.

ExamNo. of QuestionsDifficulty
SSC CGL / CHSL1–2Easy
IBPS PO / SBI PO1–2Moderate
RRB NTPC / Group D1Easy
State PSC / Police1–2Moderate

Algebraic Identities Quantitative Aptitude Short Notes

Some of the commonly used identities while solving algebra problems are as follows:

Algebraic Identities

Concepts Used in Algebraic Identities Questions

Some of the commonly used concepts in algebraic identities are as follows:

Algebraic Identities

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:

Algebraic Identities

Use pattern-matching to directly apply them instead of full expansion.

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Algebraic Identities Tricks for SSC CGL and Other Exams

Some of the quick strategies to solve identity-based problems faster:

  1. Identify the structure: Match question with standard form
  2. Avoid expansion: Use identities, don’t manually multiply
  3. Use substitution: Assign values like a=2, b=1if options are value-based
  4. Compare options: Eliminate wrong expressions via reverse checking
  5. Recognize cube and square forms immediately in expressions
  6. 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)

Algebraic Identities

IBPS PO Prelims 2024 – Mock Test

Algebraic Identities

RRB NTPC 2024 CBT 1 (Based on memory)

Algebraic Identities

Algebraic Identities Concepts for Bank Exams

Bank exams like IBPS PO and SBI PO frequently include twist-based identity questions.

Example:

Algebraic Identities

Common Mistakes to Avoid while Solving Algebraic Identities

While solving Algebraic Identities Quantitative Aptitude questions, candidates must keep the below details in mind:

  1. Forgetting signs: Misplacing ‘+’ or ‘−’ leads to incorrect simplification.
  2. Expanding instead of using identity: Wastes time and increases error chances.
  3. Wrong identity matching: Misapplying cube for square identities.
  4. Calculation errors: Skipping steps or missing multiplication leads to wrong answers.
  5. Confusing a^2 – b^2 with (a-b)^2: Remember the formulas distinctly.
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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

Q1. How are algebraic identities different from algebraic expressions?

Identities always hold true, while expressions need evaluation and may not be equal.

Q2. Why are algebraic identities important in exams?

They simplify complex expressions and save time during problem-solving.

Q3. What type of questions are usually based on identities?

Simplification, factorization, and expression comparison are common types.

Q4. Do I need to memorize all algebraic identities?

You should remember the most common ones the rest can be derived with practice.

Q5. What is the biggest mistake students make in this topic?

Trying to expand or solve without recognizing that an identity can simplify it.