बीजगणित के सूत्र  (Algebra Formulas)

बीजगणित के सूत्र  (Algebra Formulas)

1. (a + b)2 = a2 + 2ab + b2

2. (a – b)2 = a2 – 2ab + b2

3. ( a – b)2 = (a + b)2 – 4ab

4. (a + b)2 = (a – b)2 + 4ab

5. a2 + b2 = (a + b)2 – 2ab

6. a2 + b2 = (a – b)2 + 2ab

7. a2 – b2 = (a + b)(a – b)

8. (a + b)3 = a3 + 3a2b + 3ab2 + b3

9. (a + b)3 = a3 + b3 + 3ab(a + b)

10. (a – b)3 = a3 – 3a2b + 3ab2 – b3

11. (a – b)3 = a3 – b3 – 3ab(a – b)

12. a3 + b3 = (a + b)(a2 – ab + b2) 

13. a3 + b3 = (a + b)3 – 3ab(a + b)

14. a3 – b3 = (a – b)(a2 + ab + b2)

15. a3 – b3 = (a – b)3 + 3ab(a – b)

16. यदि a + b + c = 0 तो a3 + b3 + c3 = 3abc

17. a2(b – c) + b2(c – a) + c2(a – b) = – (b – c)(c – a)(a – b)

18. bc(b – c) + ca(c – a) + ab(a – b) = – (b – c)(c – a)(a – b)

19. a(b2 – c2) + b(c2 – a2) + c(a2 – b2) = (b – c)(c – a)(a – b)

20. a2 + b2 + c2 – ab – bc – ca = ½[(a – b)2 + (b – c)2 + (c – a)2]

21. (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4

22. (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4

23. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac

24. (a – b – c)2 = a2 – b2 – c2 – 2ab + 2bc – 2ac

25. (a + b + c)3 = a3 + b3 + c3 + 3(a + b)(b + c)(c + a)

26. a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ac)

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