SOLUTION: Find,in ascending powers of x,the first 4 terms in the expansion of {{{(expr(1/2)x - 2x^2)^8}}} .

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Question 1185804: Find,in ascending powers of x,the first 4 terms in the expansion of
%28expr%281%2F2%29x+-+2x%5E2%29%5E8 .

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The first four terms of %28A%2BB%29%5EN are

C%28N%2C0%29A%5EN%2AB%5E0%22%22%2B%22%22C%28N%2C1%29A%5E%28N-1%29%2AB%5E1%22%22%2B%22%22C%28N%2C2%29A%5E%28N-2%29%2AB%5E2%22%22%2B%22%22C%28N%2C3%29A%5E%28N-3%29%2AB%5E3%22%22%2B%22%22%22%22%2A%22%22%2A%22%22%2A%22%22

%28expr%281%2F2%29x+-+2x%5E2%29%5E8 is in ascending powers so we leave it as it is

Plug in and simplify with N=8, A=expr%281%2F2%29x, B=-2x%5E2.

C%288%2C0%29%28expr%281%2F2%29x%29%5E8%2A%28-2x%5E2%29%5E0%22%22%2B%22%22C%288%2C1%29%28expr%281%2F2%29x%29%5E%288-1%29%2A%28-2x%5E2%29%5E1%22%22%2B%22%22C%288%2C2%29%28expr%281%2F2%29x%29%5E%288-2%29%2A%28-2x%5E2%29%5E2%22%22%2B%22%22C%288%2C3%29%28expr%281%2F2%29x%29%5E%288-3%29%2A%28-2x%5E2%29%5E3%22%22%2B%22%22%22%22%2A%22%22%2A%22%22%2A%22%22

%281%29%281%2F2%29%5E8%2Ax%5E8%2A%281%29%22%22%2B%22%22%288%29%28expr%281%2F2%29x%29%5E%287%29%2A%28-2%29x%5E2%22%22%2B%22%22%2828%29%28expr%281%2F2%29x%29%5E%286%29%2A%28-2%29%5E2x%5E4%22%22%2B%22%22%2856%29%28expr%281%2F2%29x%29%5E%285%29%2A%28-2%29%5E3%2Ax%5E6%22%22%2B%22%22%22%22%2A%22%22%2A%22%22%2A%22%22

%281%2F2%29%5E8%2Ax%5E8%22%22-%22%22%2816%29%281%2F2%29%5E7%2Ax%5E7%2Ax%5E2%22%22%2B%22%22%2828%29%281%2F2%29%5E6x%5E6%2A%28-2%29%5E2%2Ax%5E4%22%22%2B%22%22%2856%29%281%2F2%29%5E5%2Ax%5E5%2A%28-2%29%5E3%2Ax%5E6%22%22%2B%22%22%22%22%2A%22%22%2A%22%22%2A%22%22

%281%2F2%29%5E8%2Ax%5E8%22%22-%22%22%2816%29%281%2F2%29%5E7%2Ax%5E7%2Ax%5E2%22%22%2B%22%22%2828%29%281%2F2%29%5E6x%5E6%2A%28-2%29%5E2%2Ax%5E4%22%22%2B%22%22%2856%29%281%2F2%29%5E5%2Ax%5E5%2A%28-8%29%2Ax%5E6%22%22%2B%22%22%22%22%2A%22%22%2A%22%22%2A%22%22

%281%2F2%29%5E8%2Ax%5E8%22%22-%22%22%2816%29%281%2F2%29%5E7%2Ax%5E9%22%22%2B%22%22%2828%29%281%2F2%29%5E6%2A%284%29x%5E10%22%22-%22%22%28448%29%281%2F2%29%5E5%2Ax%5E11%22%22%2B%22%22%22%22%2A%22%22%2A%22%22%2A%22%22

%281%2F2%29%5E8%2Ax%5E8%22%22-%22%22%2816%29%281%2F2%29%5E7%2Ax%5E9%22%22%2B%22%22%28112%29%281%2F2%29%5E6%2Ax%5E10%22%22-%22%22%28448%29%281%2F2%29%5E5%2Ax%5E11%22%22%2B%22%22%22%22%2A%22%22%2A%22%22%2A%22%22

%281%2F256%29%2Ax%5E8%22%22-%22%22%2816%29%281%2F128%29%2Ax%5E9%22%22%2B%22%22%28112%29%281%2F64%29%2Ax%5E10%22%22-%22%22%28448%29%281%2F32%29%2Ax%5E11%22%22%2B%22%22%22%22%2A%22%22%2A%22%22%2A%22%22

%281%2F256%29%2Ax%5E8%22%22-%22%22%2816%2F128%29%2Ax%5E9%22%22%2B%22%22%28112%2F64%29%2Ax%5E10%22%22-%22%22%28448%2F32%29%2Ax%5E11%22%22%2B%22%22%22%22%2A%22%22%2A%22%22%2A%22%22

%281%2F256%29%2Ax%5E8%22%22-%22%22%281%2F8%29%2Ax%5E9%22%22%2B%22%22%287%2F4%29%2Ax%5E10%22%22-%22%2214%2Ax%5E11%22%22%2B%22%22%22%22%2A%22%22%2A%22%22%2A%22%22

x%5E8%2F256%5E%22%22%22%22-%22%22x%5E9%2F8%5E%22%22%22%22%2B%22%227x%5E10%2F4%5E%22%22%22%22-%22%2214x%5E11%22%22%2B%22%22%22%22%2A%22%22%2A%22%22%2A%22%22

Edwin