Important formulas of maths for competitive exams

Important formulas of maths for competitive exams

(a + b)(a – b) = a2 – b2
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
(a ± b)2 = a2 + b2± 2ab
(a + b + c + d)2 = a2 + b2 + c2 + d2 + 2(ab + ac + ad + bc + bd + cd)
(a ± b)3 = a3 ± b3 ± 3ab(a ± b)
(a ± b)(a2 + b2 m ab) = a3 ± b3
(a + b + c)(a2 + b2 + c2 -ab – bc – ca) = a3 + b3 + c3 – 3abc =1/2 (a + b + c)[(a – b)2 + (b – c)2 + (c – a)2]
when a + b + c = 0, a3 + b3 + c3 = 3abc
(x + a)(x + b) (x + c) = x3 + (a + b + c) x2 + (ab + bc + ac)x + abc(x – a)(x – b) (x – c) = x3 – (a + b + c) x2 + (ab + bc + ac)x – abc
a4 + a2b2 + b4 = (a2 + ab + b2)( a2 – ab + b2)
a4 + b4 = (a2 – √2ab + b2)( a2 + √2ab + b2)an + bn = (a + b) (a n-1 – a n-2 b +  a n-3 b2 – a n-4 b3 +…….. + b n-1), (valid only if n is odd)an – bn = (a – b) (a n-1 + a n-2 b +  a n-3 b2 + a n-4 b3 +……… + b n-1), {where n ϵ N)(a ± b)2n is always positive while -(a ± b)2n is always negative, for any real values of a and b
(a – b)2n = (b – a)2” and (a – b)2n+1 = – (b – a)2n+1