बीजगणित के सूत्र & Algebra Formulas 2023
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)