展開する 1/((x+1)(x+2)^2(x^2+1)(x^2+2)^2)

解

展開する

\frac{1}{( x + 1 ) ( x + 2 ) ^{2} ( x ^{2} + 1 ) ( x ^{2} + 2 ) ^{2}}

\frac{1}{x ^{9} + 5 x ^{8} + 13 x ^{7} + 29 x ^{6} + 48 x ^{5} + 60 x ^{4} + 68 x ^{3} + 52 x ^{2} + 32 x + 16}

解答ステップ

\frac{1}{( x + 1 ) ( x + 2 ) ^{2} ( x ^{2} + 1 ) ( x ^{2} + 2 ) ^{2}}

(x + 2)^{2} = x^{2} + 4 x + 4

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

(x^{2} + 2)^{2} = x^{4} + 4 x^{2} + 4

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

拡張

(x + 1) (x^{2} + 4 x + 4) (x^{2} + 1) (x^{4} + 4 x^{2} + 4) : x^{9} + 5 x^{8} + 13 x^{7} + 29 x^{6} + 48 x^{5} + 60 x^{4} + 68 x^{3} + 52 x^{2} + 32 x + 16

= \frac{1}{x ^{9} + 5 x ^{8} + 13 x ^{7} + 29 x ^{6} + 48 x ^{5} + 60 x ^{4} + 68 x ^{3} + 52 x ^{2} + 32 x + 16}