展開する ((4x^2-16x+7)^5)/(40)

解

展開する

\frac{( 4 x ^{2} - 16 x + 7 ) ^{5}}{40}

\frac{128 x ^{10}}{5} - 512 x^{9} + 4320 x^{8} - 19968 x^{7} + 55056 x^{6} - \frac{464832 x ^{5}}{5} + 96348 x^{4} - 61152 x^{3} + \frac{46305 x ^{2}}{2} - 4802 x + \frac{16807}{40}

解答ステップ

\frac{( 4 x ^{2} - 16 x + 7 ) ^{5}}{40}

(4 x^{2} - 16 x + 7)^{5} = 1024 x^{10} - 20480 x^{9} + 172800 x^{8} - 798720 x^{7} + 2202240 x^{6} - 3718656 x^{5} + 3853920 x^{4} - 2446080 x^{3} + 926100 x^{2} - 192080 x + 16807

= \frac{1024 x ^{10} - 20480 x ^{9} + 172800 x ^{8} - 798720 x ^{7} + 2202240 x ^{6} - 3718656 x ^{5} + 3853920 x ^{4} - 2446080 x ^{3} + 926100 x ^{2} - 192080 x + 16807}{40}

分数の規則を適用する:

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

\frac{1024 x ^{10} - 20480 x ^{9} + 172800 x ^{8} - 798720 x ^{7} + 2202240 x ^{6} - 3718656 x ^{5} + 3853920 x ^{4} - 2446080 x ^{3} + 926100 x ^{2} - 192080 x + 16807}{40} = \frac{1024 x ^{10}}{40} - \frac{20480 x ^{9}}{40} + \frac{172800 x ^{8}}{40} - \frac{798720 x ^{7}}{40} + \frac{2202240 x ^{6}}{40} - \frac{3718656 x ^{5}}{40} + \frac{3853920 x ^{4}}{40} - \frac{2446080 x ^{3}}{40} + \frac{926100 x ^{2}}{40} - \frac{192080 x}{40} + \frac{16807}{40}

= \frac{1024 x ^{10}}{40} - \frac{20480 x ^{9}}{40} + \frac{172800 x ^{8}}{40} - \frac{798720 x ^{7}}{40} + \frac{2202240 x ^{6}}{40} - \frac{3718656 x ^{5}}{40} + \frac{3853920 x ^{4}}{40} - \frac{2446080 x ^{3}}{40} + \frac{926100 x ^{2}}{40} - \frac{192080 x}{40} + \frac{16807}{40}

\frac{1024 x ^{10}}{40} = \frac{128 x ^{10}}{5}

\frac{20480 x ^{9}}{40} = 512 x^{9}

\frac{172800 x ^{8}}{40} = 4320 x^{8}

\frac{798720 x ^{7}}{40} = 19968 x^{7}

\frac{2202240 x ^{6}}{40} = 55056 x^{6}

\frac{3718656 x ^{5}}{40} = \frac{464832 x ^{5}}{5}

\frac{3853920 x ^{4}}{40} = 96348 x^{4}

\frac{2446080 x ^{3}}{40} = 61152 x^{3}

\frac{926100 x ^{2}}{40} = \frac{46305 x ^{2}}{2}

\frac{192080 x}{40} = 4802 x

= \frac{128 x ^{10}}{5} - 512 x^{9} + 4320 x^{8} - 19968 x^{7} + 55056 x^{6} - \frac{464832 x ^{5}}{5} + 96348 x^{4} - 61152 x^{3} + \frac{46305 x ^{2}}{2} - 4802 x + \frac{16807}{40}