# Equations Formulae

Important Basic Formulas in Equations:

1. (a + b)(a – b) = a2 – b2
2. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
3. (a ± b)2 = a2 + b2± 2ab
4. (a + b + c + d)2 = a2 + b2 + c2 + d2 + 2(ab + ac + ad + bc + bd + cd)
5. (a ± b)3 = a3 ± b3 ± 3ab(a ± b)
6. (a ± b)(a2 + b2 m ab) = a3 ± b3
7. (a + b + c)(a2 + b2 + c2 -ab – bc – ca) = a3 + b3 + c3 – 3abc =
8. 1/2 (a + b + c)[(a - b)2 + (b - c)2 + (c - a)2]
9. when a + b + c = 0, a3 + b3 + c3 = 3abc
10. (x + a)(x + b) (x + c) = x3 + (a + b + c) x2 + (ab + bc + ac)x + abc
11. (x – a)(x – b) (x – c) = x3 – (a + b + c) x2 + (ab + bc + ac)x – abc
12. a4 + a2b2 + b4 = (a2 + ab + b2)( a2 – ab + b2)
13. a4 + b4 = (a2 – √2ab + b2)( a2 + √2ab + b2)
14. 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)
15. an – bn = (a – b) (a n-1 + a n-2 b +  a n-3 b2 + a n-4 b3 +……… + b n-1){were n ϵ N)
16. (a ± b)2n is always positive while -(a ± b)2n is always negative, for any real values of a and b
17. (a – b)2n = (b – a)2” and (a – b)2n+1 = – (b – a)2n+1
18. 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.