Bank Exam Squares, Cubes & Algebraic Identities – Page 4 (Premium Guide)
Fast Calculation • Identities • Advanced Tricks • Exam Strategy
Core Formulas
(a + b)² = a² + 2ab + b²
(a − b)² = a² − 2ab + b²
a² − b² = (a − b)(a + b)
(a + b)³ = a³ + b³ + 3ab(a + b)
Squares Shortcut Techniques
Q1. 48²
= (50 − 2)²
= 2500 − 200 + 4 = 2304
Q2. 52²
= (50 + 2)²
= 2500 + 200 + 4 = 2704
Q3. 99²
= (100 − 1)²
= 10000 − 200 + 1 = 9801
Q4. 101²
= (100 + 1)²
= 10000 + 200 + 1 = 10201
Q5. 75²
= (70 + 5)²
= 4900 + 700 + 25 = 5625
Cubes Shortcut Techniques
Q6. 12³
= 1728
Q7. 15³
= 3375
Q8. 20³
= 8000
Q9. 11³
= 1331
Q10. 25³
= 15625
Algebraic Identity Applications
Q11. 52² − 48²
= (52 − 48)(52 + 48)
= 4 × 100 = 400
Q12. 49 × 51
= (50 − 1)(50 + 1)
= 2500 − 1 = 2499
Q13. 98 × 102
= (100 − 2)(100 + 2)
= 10000 − 4 = 9996
Q14. 75 × 75
= 75² = 5625
Q15. 48 × 52
= (50 − 2)(50 + 2)
= 2500 − 4 = 2496
Topper Tips
- Convert numbers near base values (50, 100)
- Use identities instead of multiplication
- Memorize squares up to 30
- Memorize cubes up to 20
Exam Strategy
- Solve square-based questions quickly
- Use identity-based elimination
- Avoid long multiplication
Final Tip
Recognize Pattern → Apply Identity → Solve Instantly
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