Question

Expand $(1-2x-2x^2{)}^{\frac{1}{4}}$ as far as $x^2$.

Answer 1

$(1-2x-2x^2{)}^{\frac{1}{4}}=1-\frac{1}{4}(2x+2x^2)+\frac{\left(\frac{1}{4}\right)(-\frac{3}{4})}{1\cdot 2}(2x+2x^2{)}^2\dots \dots$

$=1-\frac{1}{2}x-\frac{1}{2}{x}^2-\frac{3}{8}{x}^2=1-\frac{1}{2}x-\frac{7}{8}{x}^2$