展開する (x^2(x+1)^3)/((x-7)(x+3)^2(-x^2-1))

解

展開する

\frac{x ^{2} ( x + 1 ) ^{3}}{( x - 7 ) ( x + 3 ) ^{2} ( - x ^{2} - 1 )}

\frac{x ^{5} + 3 x ^{4} + 3 x ^{3} + x ^{2}}{- x ^{5} + x ^{4} + 32 x ^{3} + 64 x ^{2} + 33 x + 63}

解答ステップ

\frac{x ^{2} ( x + 1 ) ^{3}}{( x - 7 ) ( x + 3 ) ^{2} ( - x ^{2} - 1 )}

(x + 3)^{2} = x^{2} + 6 x + 9

= \frac{x ^{2} ( x + 1 ) ^{3}}{( x - 7 ) ( x ^{2} + 6 x + 9 ) ( - x ^{2} - 1 )}

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

= \frac{x ^{2} ( x ^{3} + 3 x ^{2} + 3 x + 1 )}{( x - 7 ) ( x ^{2} + 6 x + 9 ) ( - x ^{2} - 1 )}

拡張

(x - 7) (x^{2} + 6 x + 9) (- x^{2} - 1) : - x^{5} + x^{4} + 32 x^{3} + 64 x^{2} + 33 x + 63

= \frac{x ^{2} ( x ^{3} + 3 x ^{2} + 3 x + 1 )}{- x ^{5} + x ^{4} + 32 x ^{3} + 64 x ^{2} + 33 x + 63}

拡張

x^{2} (x^{3} + 3 x^{2} + 3 x + 1) : x^{5} + 3 x^{4} + 3 x^{3} + x^{2}

= \frac{x ^{5} + 3 x ^{4} + 3 x ^{3} + x ^{2}}{- x ^{5} + x ^{4} + 32 x ^{3} + 64 x ^{2} + 33 x + 63}