展開する ((4z-7)^4)/(80)

解

展開する

\frac{( 4 z - 7 ) ^{4}}{80}

\frac{16 z ^{4}}{5} - \frac{112 z ^{3}}{5} + \frac{294 z ^{2}}{5} - \frac{343 z}{5} + \frac{2401}{80}

解答ステップ

\frac{( 4 z - 7 ) ^{4}}{80}

(4 z - 7)^{4} = 256 z^{4} - 1792 z^{3} + 4704 z^{2} - 5488 z + 2401

= \frac{256 z ^{4} - 1792 z ^{3} + 4704 z ^{2} - 5488 z + 2401}{80}

分数の規則を適用する:

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

\frac{256 z ^{4} - 1792 z ^{3} + 4704 z ^{2} - 5488 z + 2401}{80} = \frac{256 z ^{4}}{80} - \frac{1792 z ^{3}}{80} + \frac{4704 z ^{2}}{80} - \frac{5488 z}{80} + \frac{2401}{80}

= \frac{256 z ^{4}}{80} - \frac{1792 z ^{3}}{80} + \frac{4704 z ^{2}}{80} - \frac{5488 z}{80} + \frac{2401}{80}

\frac{256 z ^{4}}{80} = \frac{16 z ^{4}}{5}

\frac{1792 z ^{3}}{80} = \frac{112 z ^{3}}{5}

\frac{4704 z ^{2}}{80} = \frac{294 z ^{2}}{5}

\frac{5488 z}{80} = \frac{343 z}{5}

= \frac{16 z ^{4}}{5} - \frac{112 z ^{3}}{5} + \frac{294 z ^{2}}{5} - \frac{343 z}{5} + \frac{2401}{80}