展開する (64(s+10)(s+50))/((s)^2(s+100)^2(s+400))

解

展開する

\frac{64 ( s + 10 ) ( s + 50 )}{( s ) ^{2} ( s + 100 ) ^{2} ( s + 400 )}

\frac{64 s ^{2} + 3840 s + 32000}{s ^{5} + 600 s ^{4} + 90000 s ^{3} + 4000000 s ^{2}}

解答ステップ

\frac{64 ( s + 10 ) ( s + 50 )}{s ^{2} ( s + 100 ) ^{2} ( s + 400 )}

(s + 100)^{2} = s^{2} + 200 s + 10000

= \frac{64 ( s + 10 ) ( s + 50 )}{s ^{2} ( s ^{2} + 200 s + 10000 ) ( s + 400 )}

拡張

s^{2} (s^{2} + 200 s + 10000) (s + 400) : s^{5} + 600 s^{4} + 90000 s^{3} + 4000000 s^{2}

= \frac{64 ( s + 10 ) ( s + 50 )}{s ^{5} + 600 s ^{4} + 90000 s ^{3} + 4000000 s ^{2}}

拡張

64 (s + 10) (s + 50) : 64 s^{2} + 3840 s + 32000

= \frac{64 s ^{2} + 3840 s + 32000}{s ^{5} + 600 s ^{4} + 90000 s ^{3} + 4000000 s ^{2}}