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.

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