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Hello Aspirants! 🙏
Algebra SSC, Banking, aur Railway jaise har bade government exam ka ek bahut hi crucial part hai. Agar aap algebraic questions ko solve karne ke liye sahi formulas ka istemaal karte hain, toh aap apna 30 se 40% time bacha sakte hain.
Lekin sirf formulas yaad karna kaafi nahi hai; unhe sahi samay par apply karna aana chahiye.
Hum aapke liye laaye hain woh Top 10 Algebra Formulas (Algebraic Identities) jo exam me baar-baar repeat hote hain aur jin par direct sawal (direct questions) banaye jaate hain. In formulas ko ratta (memorize) nahi, balki master karna hai!
1. The Foundation: Basic Squares Identities (Grundlagen)
Yeh woh formulas hain jin par seedhe aur reciprocal (vyutkram) dono tarah ke questions aate hain.
| S. No. | Formula (Identity) | Exam Tip (Kya Yaad Rakhein) |
|---|---|---|
| 1. | (a+b)^2 = a^2 + b^2 + 2ab | Isse a^2 + b^2 = (a+b)^2 – 2ab nikalta hai. |
| 2. | (a-b)^2 = a^2 + b^2 – 2ab | Isse a^2 + b^2 = (a-b)^2 + 2ab nikalta hai. |
| 3. | Difference of Squares: a^2 – b^2 = (a+b)(a-b) | Yeh sabse zyada use hone wala identity hai, khaaskar Number System ke questions mein. |
| 4. | Combination Identity: (a+b)^2 + (a-b)^2 = 2(a^2 + b^2) | Jab sawal mein a^2 + b^2 aur a^2 – b^2 dono diya ho. |
| 5. | Key Identity: (a+b)^2 – (a-b)^2 = 4ab | Isse ab ki value nikalna sabse aasan ho jaata hai. |
2. The Power of Cubes: Factorization Identities cubed_with_dots:
Cube par aadharit sawal aamtaur par mushkil lagte hain, lekin in formulas se woh 10 seconds mein solve ho jaate hain.
| S. No. | Formula (Identity) | Exam Tip (Kya Yaad Rakhein) |
|---|---|---|
| 6. | Cube Expansion: (a+b)^3 = a^3 + b^3 + 3ab(a+b) | Isse a^3 + b^3 = (a+b)^3 – 3ab(a+b) ki form yaad rakhein. |
| 7. | Cube Expansion: (a-b)^3 = a^3 – b^3 – 3ab(a-b) | Isse a^3 – b^3 = (a-b)^3 + 3ab(a-b) ki form yaad rakhein. |
| 8. | Sum of Cubes (Factorization): a^3 + b^3 = (a+b)(a^2 + b^2 – ab) | A+B wali term pehle aati hai, aur last term (ab) negative hoti hai. |
| 9. | Difference of Cubes (Factorization): a^3 – b^3 = (a-b)(a^2 + b^2 + ab) | A-B wali term pehle aati hai, aur last term (ab) positive hoti hai. |
3. The Game-Changer: The Conditional Identity 👑
Yeh woh formula hai jo lambe-lambe sawalon ko ek line mein solve kar deta hai. SSC CGL aur CHSL mein is par har saal sawal aata hai.
| S. No. | Formula (Identity) | Exam Tip (Kya Yaad Rakhein) |
|---|---|---|
| 10. | Master Conditional Identity: \mathbf{a^3 + b^3 + c^3 – 3abc = (a+b+c)(a^2 + b^2 + c^2 – ab – bc – ca)} | Is identity ka sabse important case neeche diya gaya hai. |
🎯 Special Case for Formula 10: The Ultimate ShortcutAgar aapko sawal mein diya ho ki a+b+c = 0, toh poora right-hand side (RHS) zero ho jaata hai.
Yeh sabse bada shortcut hai! Exam mein jab bhi teen terms ka sum zero ho, toh unke cubes ka sum 3abc hota hai. Is par hamesha questions aate hain.
Aapki Taiyaari Ka Next Step ➡️
Sirf yeh 10 formulas padh lena kaafi nahi hai. Inhe aage ki practice mein use karna zaroori hai.
- Daily Practice: Roz 15-20 minutes in formulas par based Previous Year Questions (PYQs) solve karein.
- Formula Sheet: In sabhi formulas ki ek alag se sheet bana kar apni study desk par chipka lein.
Remember: Algebra marks score karne ka sabse aasan tareeka hai, agar aapki formulas par pakad mazboot ho. All the best! 👍
