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12/24/2017 Các đẳng thức đáng nhớ cần nhớ - Đại số - Diễn đàn Toán học (1) (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac (2) (a + b − c)2 = a2 + b2 + c2 + 2ab − 2bc − 2ac (3) (a − b − c)2 = a2 + b2 + c2 − 2ab − 2ac + 2bc (4) a3 + b3 = (a + b)3 − 3ab(a + b) (5) a3 − b3 = (a − b)3 + 3ab(a − b) (6) (a + b + c)3 = a3 + b3 + c3 + 3(a + b)(b + c)(c + a) (7) a3 + b3 + c3 − 3abc = (a + b + c)(a2 + b2 + c2 − ab − bc − ac) (8) (a − b)3 + (b − c)3 + (c − a)3 = 3(a − b)(b − c)(c − a) (9) (a + b)(b + c)(c + a) − 8abc = a(b − c)2 + b(c − a)2 + c(a − b)2 (10) (a + b)(b + c)(c + a) = (a + b + c)(ab + bc + ca) − abc (11) ab + bc + ca − a b − b c − c a = (a − b)3 + (b − c)3 + (c − a)3 (12)ab3 + bc3 + ca3 − a3 b − b3 c − c3 a = (a + b + c)[(a − b)3 + (b − c)3 + (c − a)3 ] 2 2 2 (13) an − bn = (a − b)(an−1 + an−2 b + an−3 b2 + +a2 bn−3 + abn−2 + bn−1 ) (14) Với n lẻ: an + bn = (a + b)(an−1 − an−2 b + an−3 b2 − +a2 bn−3 − abn−2 + bn−1 ) (15) Nhị thức Newton: (a + b)n = an + + n)! 1!(n − 1)! n! n! n! n! an−1 b + an−2 b2 + + an−k bk + + a2 bn−2 (n − 1)!1! (n − 2)!2! (n − k)!k! 2!(n − 2)! abn−1 + bn https://diendantoanhoc.net/topic/42840-c%C3%A1c-h%E1%BA%B1ng-%C4%91%E1%BA%B3ng-th%E1%BB%A9c-%C4%91%C3%A1ng-nh%E1%BB%… 1/1