(1) The document lists many important mathematical formulas related to algebra, trigonometry, geometry, and number theory. (2) Some examples include formulas for factorizing quadratic expressions, expanding products of binomials, sums and products of roots, and properties related to divisibility of numbers. (3) The formulas provide concise expressions of key relationships between mathematical quantities.

1. Important Mathematical Formulas Maths Formulas
(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
if α and β are the roots of equation ax2 + bx + c = 0, roots of cx” + bx + a = 0 are 1/α and 1/β. if α and β are the roots of
equation ax2 + bx + c = 0, roots of ax2 – bx + c = 0 are -α and -β. n(n + l)(2n + 1) is always divisible by 6. 32n leaves
remainder = 1 when divided by 8 n3 + (n + 1 )3 + (n + 2 )3 is always divisible by 9 102n + 1 + 1 is always divisible by
11 n(n2- 1) is always divisible by 6 n2+ n is always even 23n-1 is always divisible by 7 152n-1 +l is always divisible by 16
n3 + 2n is always divisible by 3 34n – 4 3n is always divisible by 17 n! + 1 is not divisible by any number between 2 and n
(where n! = n (n – l)(n – 2)(n – 3)…….3.2.1) for eg 5! = 5.4.3.2.1 = 120 and similarly 10! = 10.9.8…….2.1= 3628800
Product of n consecutive numbers is always divisible by n!. If n is a positive integer and p is a prime, then np – n is
divisible by p. |x| = x if x ≥ 0 and |x| = – x if x ≤ 0. Minimum value of a2.sec2Ɵ + b2.cosec2Ɵ is (a + b)2; (0° < Ɵ <
90°) for eg. minimum value of 49 sec2Ɵ + 64.cosec2Ɵ is (7 + 8)2 = 225. among all shapes with the same perimeter a
circle has the largest area. if one diagonal of a quadrilateral bisects the other, then it also bisects the quadrilateral. sum of
all the angles of a convex quadrilateral = (n – 2)180° number of diagonals in a convex quadrilateral = 0.5n(n – 3) let P, Q
are the midpoints of the nonparallel sides BC and AD of a trapezium ABCD.Then, ΔAPD = ΔCQB.