Some Inevitable Formulas
Square Formula and Factors:
1. (a + b)2 = a2 + 2ab + b2
2. (a - b)2 = a2 - 2ab + b2
3. a2 - b2 = (a + b) (a - b)
4. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
= a2 + b2 + c2 + 2(ab + bc + ca)
(Corollaries):
5. a2 + b2 = (a + b)2 - 2ab
6. a2 - b2 = (a - b)2 + 2ab
7. 4ab = (a + b)2 - (a - b)2
8. (a + b)2 = (a - b)2 + 4ab
9. (a - b)2 = (a + b)2 - 4ab
10. a2 + b2 + c2 = (a + b + c)2 - 2(ab + bc + ca)
11. (a + b - c)2 = a2 + b2 + c2 + 2ab - 2bc - 2ca
12. (a - b + c)2 = a2 + b2 + c2 - 2ab + 2bc - 2ca
13. (a - b - c)2 = a2 + b2 + c2 - 2ab + 2bc - 2ca
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. (x - a) (x - b) = x2 - (a + b) x + ab
Cubic Formula and their Factors:
1. (a + b)3 = a3 + 3a2b + 3ab2 + b3 = a3 + b3 + 3ab (a + b)
2. (a - b)3 = a3 - 3a2b + 3ab2 - b3 = a3 - b3 - 3ab (a - b)
3. a3 + b3 = (a + b) (a2 - ab + b2)
4. a3 + b3 = (a + b) (a2 - ab + b2)
5. a3 + b3 + c3 - 3abc = (a + b + c) (a2 + b2 + c2 - ab - bc - ca)
(Corollaries):
6. a3 + b3 = (a + b)3 - 3ab (a + b)
7. a3 + b3 = (a + b)3 - 3ab (a + b)
