L live.fast Member Joined Feb 12, 2006 Messages 501 Gender Undisclosed HSC N/A Apr 29, 2007 #1 Expand (x - (1/x) ) ^ 3 in ascending powers of x ????
ellen.louise Member Joined Mar 27, 2007 Messages 516 Location Locked in my cupboard Gender Female HSC 2007 Apr 29, 2007 #2 live.fast said: Expand (x - (1/x) ) ^ 3 in ascending powers of x ???? Click to expand... ok... =(x - (1/x))(x^2 - 2 + (1/x^2)) =x^3 - 2x + 1/x - x + 2/x - 1/x^3 =x^3 - 3x + 3x^-1 - x^-3 = - x^-3 + 3x^-1 - 3x + x^3 Ascending powers of x is just the order you arrange it in at the end.
live.fast said: Expand (x - (1/x) ) ^ 3 in ascending powers of x ???? Click to expand... ok... =(x - (1/x))(x^2 - 2 + (1/x^2)) =x^3 - 2x + 1/x - x + 2/x - 1/x^3 =x^3 - 3x + 3x^-1 - x^-3 = - x^-3 + 3x^-1 - 3x + x^3 Ascending powers of x is just the order you arrange it in at the end.
P pLuvia Guest Apr 29, 2007 #3 Using binomial (x-(1/x)3 =(3C0*(-1/x)3+3C1*x*(-1/x)2+3C2*x2*(-1/x)+3C3*x3) Simplify