展開する ((6-2x)^4)/(108)

解

展開する

\frac{( 6 - 2 x ) ^{4}}{108}

\frac{4 x ^{4}}{27} - \frac{16 x ^{3}}{9} + 8 x^{2} - 16 x + 12

解答ステップ

\frac{( 6 - 2 x ) ^{4}}{108}

(6 - 2 x)^{4} = 1296 - 1728 x + 864 x^{2} - 192 x^{3} + 16 x^{4}

= \frac{1296 - 1728 x + 864 x ^{2} - 192 x ^{3} + 16 x ^{4}}{108}

因数

1296 - 1728 x + 864 x^{2} - 192 x^{3} + 16 x^{4} : 16 (81 - 108 x + 54 x^{2} - 12 x^{3} + x^{4})

= \frac{16 ( 81 - 108 x + 54 x ^{2} - 12 x ^{3} + x ^{4} )}{108}

共通因数を約分する:

4

= \frac{4 ( x ^{4} - 12 x ^{3} + 54 x ^{2} - 108 x + 81 )}{27}

拡張

4 (x^{4} - 12 x^{3} + 54 x^{2} - 108 x + 81) : 4 x^{4} - 48 x^{3} + 216 x^{2} - 432 x + 324

= \frac{4 x ^{4} - 48 x ^{3} + 216 x ^{2} - 432 x + 324}{27}

分数の規則を適用する:

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

\frac{4 x ^{4} - 48 x ^{3} + 216 x ^{2} - 432 x + 324}{27} = \frac{4 x ^{4}}{27} - \frac{48 x ^{3}}{27} + \frac{216 x ^{2}}{27} - \frac{432 x}{27} + \frac{324}{27}

= \frac{4 x ^{4}}{27} - \frac{48 x ^{3}}{27} + \frac{216 x ^{2}}{27} - \frac{432 x}{27} + \frac{324}{27}

\frac{48 x ^{3}}{27} = \frac{16 x ^{3}}{9}

\frac{216 x ^{2}}{27} = 8 x^{2}

\frac{432 x}{27} = 16 x

\frac{324}{27} = 12

= \frac{4 x ^{4}}{27} - \frac{16 x ^{3}}{9} + 8 x^{2} - 16 x + 12