展開する (8(2x^2-8x-1))/(3x^{4/3)(x+1)^3}

解

展開する

\frac{8 ( 2 x ^{2} - 8 x - 1 )}{3 x ^{\frac{4}{3}} ( x + 1 ) ^{3}}

\frac{16 x ^{2} - 64 x - 8}{3 x ^{\frac{13}{3}} + 9 x ^{\frac{10}{3}} + 9 x ^{\frac{7}{3}} + 3 x ^{\frac{4}{3}}}

解答ステップ

\frac{8 ( 2 x ^{2} - 8 x - 1 )}{3 x ^{\frac{4}{3}} ( x + 1 ) ^{3}}

(x + 1)^{3} = x^{3} + 3 x^{2} + 3 x + 1

= \frac{8 ( 2 x ^{2} - 8 x - 1 )}{3 x ^{\frac{4}{3}} ( x ^{3} + 3 x ^{2} + 3 x + 1 )}

拡張

3 x^{\frac{4}{3}} (x^{3} + 3 x^{2} + 3 x + 1) : 3 x^{\frac{13}{3}} + 9 x^{\frac{10}{3}} + 9 x^{\frac{7}{3}} + 3 x^{\frac{4}{3}}

= \frac{8 ( 2 x ^{2} - 8 x - 1 )}{3 x ^{\frac{13}{3}} + 9 x ^{\frac{10}{3}} + 9 x ^{\frac{7}{3}} + 3 x ^{\frac{4}{3}}}

拡張

8 (2 x^{2} - 8 x - 1) : 16 x^{2} - 64 x - 8

= \frac{16 x ^{2} - 64 x - 8}{3 x ^{\frac{13}{3}} + 9 x ^{\frac{10}{3}} + 9 x ^{\frac{7}{3}} + 3 x ^{\frac{4}{3}}}