[STEP][剑桥数学入学考试][00-S1-Q2][Binomial coefficient][P1] STEP

casperyc的马甲 5月前 343

  • Show that the coefficient of $x^{-12}$ in the expansion of
    $$
    \left(x^{4}-\frac{1}{x^{2}}\right)^{5}
    \left(x-\frac{1}{x}\right)^{6}
    $$
    is $-15$, and calculate the coefficient of $x^2$.
  • Hence, or otherwise, calculate the coefficients of $x^4$ and $x^{38}$ in the expansion of $$ (x^2-1)^{11}(x^4+x^2+1)^5. $$
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