展開する (x^2-c(x-1/(sqrt(pi)))-1/2)^2

解

展開する

(x^{2} - c (x - \frac{1}{π}) - \frac{1}{2})^{2}

\frac{1}{4} - \frac{c}{π} - \frac{2 c ^{2} x}{π} + \frac{2 c x ^{2}}{π} + \frac{c ^{2}}{π} - 2 c x^{3} - x^{2} + x^{4} + c^{2} x^{2} + c x

解答ステップ

(x^{2} - c (x - \frac{1}{π}) - \frac{1}{2})^{2}

拡張

x^{2} - c (x - \frac{1}{π}) - \frac{1}{2} : x^{2} - c x + \frac{c}{π} - \frac{1}{2}

= (x^{2} - c x + \frac{c}{π} - \frac{1}{2})^{2}

(x^{2} - c x + \frac{c}{π} - \frac{1}{2})^{2} = (x^{2} - c x + \frac{c}{π} - \frac{1}{2}) (x^{2} - c x + \frac{c}{π} - \frac{1}{2})

= (x^{2} - c x + \frac{c}{π} - \frac{1}{2}) (x^{2} - c x + \frac{c}{π} - \frac{1}{2})

拡張

(x^{2} - c x + \frac{c}{π} - \frac{1}{2}) (x^{2} - c x + \frac{c}{π} - \frac{1}{2}) : \frac{1}{4} + \frac{- π c - 2 π c ^{2} x + 2 π c x ^{2} + c ^{2} - 2 π c x ^{3} - π x ^{2} + π x ^{4} + π c ^{2} x ^{2} + π c x}{π}

= \frac{1}{4} + \frac{- π c - 2 π c ^{2} x + 2 π c x ^{2} + c ^{2} - 2 π c x ^{3} - π x ^{2} + π x ^{4} + π c ^{2} x ^{2} + π c x}{π}

分数の規則を適用する:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{- π c - 2 π c ^{2} x + 2 π c x ^{2} + c ^{2} - 2 π c x ^{3} - π x ^{2} + π x ^{4} + π c ^{2} x ^{2} + π c x}{π} = - \frac{π c}{π} - \frac{2 π c ^{2} x}{π} + \frac{2 π c x ^{2}}{π} + \frac{c ^{2}}{π} - \frac{2 π c x ^{3}}{π} - \frac{π x ^{2}}{π} + \frac{π x ^{4}}{π} + \frac{π c ^{2} x ^{2}}{π} + \frac{π c x}{π}

= \frac{1}{4} - \frac{π c}{π} - \frac{2 π c ^{2} x}{π} + \frac{2 π c x ^{2}}{π} + \frac{c ^{2}}{π} - \frac{2 π c x ^{3}}{π} - \frac{π x ^{2}}{π} + \frac{π x ^{4}}{π} + \frac{π c ^{2} x ^{2}}{π} + \frac{π c x}{π}

\frac{π c}{π} = \frac{c}{π}

\frac{2 π c ^{2} x}{π} = \frac{2 c ^{2} x}{π}

\frac{2 π c x ^{2}}{π} = \frac{2 c x ^{2}}{π}

\frac{2 π c x ^{3}}{π} = 2 c x^{3}

\frac{π x ^{2}}{π} = x^{2}

\frac{π x ^{4}}{π} = x^{4}

\frac{π c ^{2} x ^{2}}{π} = c^{2} x^{2}

\frac{π c x}{π} = c x

= \frac{1}{4} - \frac{c}{π} - \frac{2 c ^{2} x}{π} + \frac{2 c x ^{2}}{π} + \frac{c ^{2}}{π} - 2 c x^{3} - x^{2} + x^{4} + c^{2} x^{2} + c x