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. 4ab = (a+b)²-(a-b)²
10. ab = {(a+b)/2}²-{(a-b)/2}²
11. (a+b+c)² = a²+b²+c²+2(ab+bc+ca)
12. (a+b)³ = a³+3a²b+3ab²+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. (a² + b² + c²) = (a
+ b + c)² – 2(ab + bc + ca)
21. 2 (ab + bc + ca) = (a + b + c)² – (a² + b² +
c²)
22. (a + b + c)³ = a³ + b³ + c³ + 3 (a + b) (b +
c) (c + a)
23. a³ + b³ + c³ – 3abc =(a+b+c)(a² + b²+
c²–ab–bc– ca)
24. a3 + b3 + c3 – 3abc =½ (a+b+c) {
(a–b)²+(b–c)²+(c–a)²}
25. (x + a) (x + b) =
x² + (a + b) x + ab
26. (x + a) (x – b) = x² + (a – b) x – ab
27. (x – a) (x + b) = x² + (b – a) x – ab
28. (x – a) (x – b) = x² – (a + b) x + ab
29. (x+p) (x+q) (x+r) = x³ + (p+q+r) x² +
(pq+qr+rp) x +pqr
30. bc (b-c) + ca (c- a) + ab (a - b) = - (b - c)
(c- a) (a - b)
31. a² (b- c) + b² (c- a) + c² (a - b) = -(b-c)
(c-a) (a - b)
32. a (b² - c²) + b (c² - a²) + c (a² - b²) = (b
- c) (c- a) (a - b)
33. a³ (b - c) + b³ (c-a) +c³ (a -b) =- (b-c)
(c-a) (a - b)(a + b + c)
34. b²-c² (b²-c²) +
c²a²(c²-a²)+a²b²(a²-b²)=-(b-c) (c-a) (a-b) (b+c) (c+a) (a+b)
35. (ab + bc+ca) (a+b+c) - abc = (a + b)(b + c)
(c+a)
36. (b + c)(c + a)(a + b) + abc = (a + b +c) (ab
+ bc + ca)