ষষ্ঠ থেকে দশম শ্রেণীর সকল বীজগাণিতিক সূত্রসমূহ

ষষ্ঠ থেকে দশম শ্রেণি পর্যন্ত বীজগণিতের সকল সূত্র দেওয়া হলো।

1. (a + b)²= a²+ 2ab + b²

2. (a + b)²= (a – b)²+ 4ab

3. (a – b)² = a² – 2ab + b²

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. 2 (a²+b²) = (a + b)² + (a – b)²

9. (a + b + c)² = (a² + b² + c² ) + 2 (ab + bc + ca)

10. (a² + b² + c² ) = (a + b + c)² – 2(ab + bc + ca)

11. 2 (ab + bc + ca) = (a + b + c) 2 – (a 2 + b 2 + c 2 )

12. (a + b)³ = a³+ 3a³ b + 3ab³ + b³

13. (a + b)³ = a³ + b³+ 3ab (a + b)

14. (a – b)³ = a³– 3a²b + 3ab² – b³

15. (a – b)³ = a³ – b³ – 3ab (a – b)

16. a³+ b³ = (a + b) ( a² – ab + b²)

17. a³ + b³ = (a + b)³– 3ab (a + b)

18. a³– b³ = (a – b) ( a² +ab + b²)

19. a³ – b³ = (a – b)³ + 3ab (a – b)

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

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

22. a³ + b³ + c³ – 3abc = (a + b + c) { (a – b)

2 + {(b – c)² + (c – a)² }

23. (x + a) (x + b) = x² + (a + b) x + ab

24. (x + a) (x – b) = x² + (a – b) x – ab

25. (x – a) (x + b) = x² + (b – a) x – ab

26. (x – a) (x – b) = x² – (a + b) x + ab

27. (x + p) (x + q) (x + r) = x³ + (p + q + r) x² + (pq + qr + rp) x +pqr