Mathematics Village
FORMULAE Algebra
FORMULAE
Algebra
1. (a + b)2 = a2 + b2 + 2ab
= (a - b) 2 + 4ab
2. (a- b) 2 = a2 + b2 - 2ab
= (a + b) 2 – 4ab
3. a2- b2 = (a - b) (a + b)
4. a2 + b2 = (a + b) 2 - 2ab = (a - b) 2 + 2ab
5. (a + b) 2 + (a- b) 2 = 2(a2
+ b2)
6. (a + b) 2 – (a
- b) 2 = 4ab
7. (a + b + c) 2 = a2 + b2
+ c2 + 2ab + 2bc + 2ca
8. a2 + b2 + c2 - ab - bc - ca =1/2[(a-b) 2 + (b -c) 2 + (c- a)
2]
9. (a + b)3 = a3 + b3 + 3ab
(a + b) = a3 + 3a2b + 3ab2 + b3
10. (a- b) 3 = a3 - b3 -3ab
(a -b) = a3 - 3a2b + 3ab2 - b3
11. a3 + b3 = (a + b) 3 -
3ab (a + b) = (a + b) (a2–- ab + b2)
12. a3 - b3= (a - b) 3 +
3ab (a- b) = (a- b) (a2 + ab + b2)
13. (a + b + c) 3 = a3 + b3
+ c3 + 3(a + b) (b + c) (c + a)
14. a3 + b3 + c3 – 3abc = (a + b + c) (a2 + b2 + c2
- ab - bc - ca)
If a + b + c = 0 then a3 + b3+ c3
= 3abc
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