Question 1185804
<pre>
The first four terms of {{{(A+B)^N}}} are

{{{C(N,0)A^N*B^0}}}{{{""+""}}}{{{C(N,1)A^(N-1)*B^1}}}{{{""+""}}}{{{C(N,2)A^(N-2)*B^2}}}{{{""+""}}}{{{C(N,3)A^(N-3)*B^3}}}{{{""+""}}}{{{""*""*""*""}}}

{{{(expr(1/2)x - 2x^2)^8}}} is in ascending powers so we leave it as it is

Plug in and simplify with {{{N=8}}}, {{{A=expr(1/2)x}}}, {{{B=-2x^2}}}.

{{{C(8,0)(expr(1/2)x)^8*(-2x^2)^0}}}{{{""+""}}}{{{C(8,1)(expr(1/2)x)^(8-1)*(-2x^2)^1}}}{{{""+""}}}{{{C(8,2)(expr(1/2)x)^(8-2)*(-2x^2)^2}}}{{{""+""}}}{{{C(8,3)(expr(1/2)x)^(8-3)*(-2x^2)^3}}}{{{""+""}}}{{{""*""*""*""}}}

{{{(1)(1/2)^8*x^8*(1)}}}{{{""+""}}}{{{(8)(expr(1/2)x)^(7)*(-2)x^2}}}{{{""+""}}}{{{(28)(expr(1/2)x)^(6)*(-2)^2x^4}}}{{{""+""}}}{{{(56)(expr(1/2)x)^(5)*(-2)^3*x^6}}}{{{""+""}}}{{{""*""*""*""}}}

{{{(1/2)^8*x^8}}}{{{""-""}}}{{{(16)(1/2)^7*x^7*x^2}}}{{{""+""}}}{{{(28)(1/2)^6x^6*(-2)^2*x^4}}}{{{""+""}}}{{{(56)(1/2)^5*x^5*(-2)^3*x^6}}}{{{""+""}}}{{{""*""*""*""}}}

{{{(1/2)^8*x^8}}}{{{""-""}}}{{{(16)(1/2)^7*x^7*x^2}}}{{{""+""}}}{{{(28)(1/2)^6x^6*(-2)^2*x^4}}}{{{""+""}}}{{{(56)(1/2)^5*x^5*(-8)*x^6}}}{{{""+""}}}{{{""*""*""*""}}}

{{{(1/2)^8*x^8}}}{{{""-""}}}{{{(16)(1/2)^7*x^9}}}{{{""+""}}}{{{(28)(1/2)^6*(4)x^10}}}{{{""-""}}}{{{(448)(1/2)^5*x^11}}}{{{""+""}}}{{{""*""*""*""}}}

{{{(1/2)^8*x^8}}}{{{""-""}}}{{{(16)(1/2)^7*x^9}}}{{{""+""}}}{{{(112)(1/2)^6*x^10}}}{{{""-""}}}{{{(448)(1/2)^5*x^11}}}{{{""+""}}}{{{""*""*""*""}}}

{{{(1/256)*x^8}}}{{{""-""}}}{{{(16)(1/128)*x^9}}}{{{""+""}}}{{{(112)(1/64)*x^10}}}{{{""-""}}}{{{(448)(1/32)*x^11}}}{{{""+""}}}{{{""*""*""*""}}}

{{{(1/256)*x^8}}}{{{""-""}}}{{{(16/128)*x^9}}}{{{""+""}}}{{{(112/64)*x^10}}}{{{""-""}}}{{{(448/32)*x^11}}}{{{""+""}}}{{{""*""*""*""}}}

{{{(1/256)*x^8}}}{{{""-""}}}{{{(1/8)*x^9}}}{{{""+""}}}{{{(7/4)*x^10}}}{{{""-""}}}{{{14*x^11}}}{{{""+""}}}{{{""*""*""*""}}}

{{{x^8/256^""}}}{{{""-""}}}{{{x^9/8^""}}}{{{""+""}}}{{{7x^10/4^""}}}{{{""-""}}}{{{14x^11}}}{{{""+""}}}{{{""*""*""*""}}}

Edwin</pre>