展開する 1/((s^2+2s+2))(1/((s+1)^2))

解

展開する

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

\frac{1}{s ^{4} + 4 s ^{3} + 7 s ^{2} + 6 s + 2}

解答ステップ

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

括弧を削除する:

(a) = a

= \frac{1}{s ^{2} + 2 s + 2} \cdot \frac{1}{( s + 1 ) ^{2}}

\frac{1}{( s + 1 ) ^{2}} = \frac{1}{s ^{2} + 2 s + 1}

= \frac{1}{s ^{2} + 2 s + 2} \cdot \frac{1}{s ^{2} + 2 s + 1}

分数を乗じる:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{( s ^{2} + 2 s + 2 ) ( s ^{2} + 2 s + 1 )}

数を乗じる:

1 \cdot 1 = 1

= \frac{1}{( s ^{2} + 2 s + 2 ) ( s ^{2} + 2 s + 1 )}

拡張

(s^{2} + 2 s + 2) (s^{2} + 2 s + 1) : s^{4} + 4 s^{3} + 7 s^{2} + 6 s + 2

= \frac{1}{s ^{4} + 4 s ^{3} + 7 s ^{2} + 6 s + 2}