展開する (2*(-x^4+(h+x)^4))/h

解

展開する

\frac{2 \cdot ( - x ^{4} + ( h + x ) ^{4} )}{h}

8 x^{3} + 12 x^{2} h + 8 x h^{2} + 2 h^{3}

解答ステップ

\frac{2 ( - x ^{4} + ( h + x ) ^{4} )}{h}

因数

- x^{4} + (h + x)^{4} : h ((h + x)^{2} + x^{2}) (h + 2 x)

= \frac{2 h ( ( h + x ) ^{2} + x ^{2} ) ( h + 2 x )}{h}

共通因数を約分する:

h

= 2 (x^{2} + (x + h)^{2}) (2 x + h)

拡張

x^{2} + (x + h)^{2} : 2 x^{2} + 2 x h + h^{2}

= 2 (2 x^{2} + 2 x h + h^{2}) (2 x + h)

拡張

(2 x^{2} + 2 x h + h^{2}) (2 x + h) : 4 x^{3} + 6 x^{2} h + 4 x h^{2} + h^{3}

= 2 (4 x^{3} + 6 x^{2} h + 4 x h^{2} + h^{3})

拡張

2 (4 x^{3} + 6 x^{2} h + 4 x h^{2} + h^{3}) : 8 x^{3} + 12 x^{2} h + 8 x h^{2} + 2 h^{3}

= 8 x^{3} + 12 x^{2} h + 8 x h^{2} + 2 h^{3}