Algebra Formulas
List Of Algebraic Formulas –
- (a + b)2 = a2+ b2 + 2ab
- (a – b)2 = a2 + b2 – 2ab
- a2 – b2 = (a + b) (a – b)
- (a + b)3 = a3+ b3 + 3ab (a+b)
- (a + b)3 = a3+ b3 + 3a2b + 3ab2
Basic Mathematics Formulas
- (a – b)3 = a3– b3 – 3ab(a-b)
- (a – b)3 = a3– b3 – 3a2b + 3ab2
- a3+ b3 = (a + b) (a2 + b2 – ab)
- a3– b3 = (a – b) (a2 + b2 + ab)
- (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac
- (a – b + c)2 = a2 + b2 + c2 – 2ab – 2bc + 2ac
- (a + b – c)2 = a2 + b2 + c2 + 2ab – 2bc – 2ac
- (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ac
- (-a + b + c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ac
- (-a – b + c)2 = a2 + b2 + c2 + 2ab – 2bc – 2ac
- (a – b – c)2 = a2 + b2 + c2 – 2ab – 2bc + 2ac
- (-a – b – c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac
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Proof of Algebra Formulas :-
1. (a + b)3 = a3+ b3 + 3ab (a+b)
Or
(a + b)3 = a3+ b3 + 3a2b + 3ab2
Proof :-
(a + b)3 = (a + b) (a + b)2
(a + b)3 = (a + b) (a2+ b2 + 2ab)
(a + b)3 = a (a2+ b2 + 2ab) + b (a2+ b2 + 2ab)
(a + b)3 = a3+ ab2 + 2a2b + a2b + b3 + 2ab2
(a + b)3 = a3+ b3 + 3a2b + 3ab2
Hence Proved.
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2. (a – b)3 = a3– b3 – 3ab(a-b)
Or
(a – b)3 = a3– b3 – 3a2b + 3ab2
Solve :-
(a – b)3 = (a – b) (a – b)2
(a – b)3 = (a – b) (a2 + b2 – 2ab)
(a – b)3 = a (a2 + b2 – 2ab) – b (a2 + b2 – 2ab)
(a – b)3 = a3+ ab2 – 2a2b – a2b – b3 + 2ab2
(a – b)3 = a3– b3 – 3a2b + 3ab2
