Important Math Formulas for Competitive exams

1. (a + b)(a – b) = a2 – b2

1. (a + b + c) 2 = a2 + b2 + c 2 + 2(ab + bc + ca)

1. (a ± b) 2 = a2 + b2± 2ab

1. (a + b + c + d) 2 = a2 + b 2 + c 2 + d2 + 2(ab +ac + ad + bc + bd + cd)

1. (a ± b) 3 = a3 ± b3 ± 3ab(a ± b)

1. (a ± b)(a 2 + b2 m ab) = a3 ± b 3

1. (a + b + c)(a 2 + b2 + c 2 -ab – bc – ca) = a 3+ b3 + c 3 – 3abc =
1/2 (a + b + c)[(a – b) 2 + (b – c) 2 + (c – a) 2]

1. when a + b + c = 0, a 3 + b3 + c 3 = 3abc

1. (x + a)(x + b) (x + c) = x 3 + (a + b + c) x 2 +(ab + bc + ac)x + abc
1. (x – a)(x – b) (x – c) = x 3 – (a + b + c) x 2 +(ab + bc + ac)x – abc

1. a4 + a 2b2 + b4 = (a 2 + ab + b 2)( a2 – ab + b2)

1. a4 + b 4 = (a 2 – √2ab + b2 )( a2 + √2ab + b2 )

1. an + b n = (a + b) (a n-1 – a n-2 b + a n-3 b2– a n-4 b 3 +…….. + b n-1 )
(valid only if n is odd)

1. 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)

1. (a ± b) 2n is always positive while -(a ± b) 2n is always negative, for any real values of a and b

1. (a – b) 2n = (b – a) 2” and (a – b) 2n+1 = – (b– a) 2n+1

1. if α and β are the roots of equation ax 2 + bx+ c = 0, roots of cx” + bx + a = 0 are 1/α and 1/β.

if α and β are the roots of equation ax 2 + bx + c= 0, roots of ax 2 – bx + c = 0 are -α and -β.