Basic Formula of Algebra
1. (a + b)2 = a2 +
2ab + b2
2. (a - b)2 = a2 -
2ab + b2
3. a2 + b2 = (a +
b)2 – 2ab
4. a2 + b2 = (a -
b)2 + 2ab
5. (a + b)2 = (a – b)2
+ 4ab
6. (a - b)2 = (a + b)2
- 4ab
9. (a + b+ c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
10. a2 + b2 + c2 =
(a + b + c)2 – 2(ab + bc + ca)
11. 2(ab + bc + ca) = (a + b + c)2 – (a2
+ b2 + c2)
12. (a + b) (a – b) = a2 – b2
13. (x + a) (x + b) = x2 + (a + b)x +
ab
14. (x + a) (x – b) = x2 + (a – b)x –
ab
15. (x – a) (x + b) = x2 + (a – b)x –
ab
16. (x – a) (x – b) = x2 – (a + b)x +
ab
17. (a + b)3 = a3 + 3a2b
+ 3ab2 + b3
18. (a – b)3 = a3 – 3a2b
+ 3ab2 – b3
19. a3 + b3 = (a+ b)3
– 3ab (a + b)
20. a3 – b3 = (a – b)3
+ 3ab (a – b)
21. (a + b) (a2 – ab + b2) =
a3 + b3
22. (a – b) (a2 + ab + b2)
= a3 – b3
23. (x + a) (x + b) (x + c) = x3
+ (a + b + c)x2 + (bc + ca + ab)x + abc
24. (x – a) (x – b) (x – c) = x3
– (a + b + c)x2 + (bc + ca + ab)x – abc
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