展開する ((20x^3-30x^2+12x-1)^2)/(400)

解

展開する

\frac{( 20 x ^{3} - 30 x ^{2} + 12 x - 1 ) ^{2}}{400}

x^{6} - 3 x^{5} + \frac{69 x ^{4}}{20} - \frac{19 x ^{3}}{10} + \frac{51 x ^{2}}{100} - \frac{3 x}{50} + \frac{1}{400}

解答ステップ

\frac{( 20 x ^{3} - 30 x ^{2} + 12 x - 1 ) ^{2}}{400}

(20 x^{3} - 30 x^{2} + 12 x - 1)^{2} = 400 x^{6} - 1200 x^{5} + 1380 x^{4} - 760 x^{3} + 204 x^{2} - 24 x + 1

= \frac{400 x ^{6} - 1200 x ^{5} + 1380 x ^{4} - 760 x ^{3} + 204 x ^{2} - 24 x + 1}{400}

分数の規則を適用する:

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

\frac{400 x ^{6} - 1200 x ^{5} + 1380 x ^{4} - 760 x ^{3} + 204 x ^{2} - 24 x + 1}{400} = \frac{400 x ^{6}}{400} - \frac{1200 x ^{5}}{400} + \frac{1380 x ^{4}}{400} - \frac{760 x ^{3}}{400} + \frac{204 x ^{2}}{400} - \frac{24 x}{400} + \frac{1}{400}

= \frac{400 x ^{6}}{400} - \frac{1200 x ^{5}}{400} + \frac{1380 x ^{4}}{400} - \frac{760 x ^{3}}{400} + \frac{204 x ^{2}}{400} - \frac{24 x}{400} + \frac{1}{400}

\frac{400 x ^{6}}{400} = x^{6}

\frac{1200 x ^{5}}{400} = 3 x^{5}

\frac{1380 x ^{4}}{400} = \frac{69 x ^{4}}{20}

\frac{760 x ^{3}}{400} = \frac{19 x ^{3}}{10}

\frac{204 x ^{2}}{400} = \frac{51 x ^{2}}{100}

\frac{24 x}{400} = \frac{3 x}{50}

= x^{6} - 3 x^{5} + \frac{69 x ^{4}}{20} - \frac{19 x ^{3}}{10} + \frac{51 x ^{2}}{100} - \frac{3 x}{50} + \frac{1}{400}