展开 (s+4)(s+1/2)(s+6/5)(s+5/2)

解答

展开

(s + 4) (s + \frac{1}{2}) (s + \frac{6}{5}) (s + \frac{5}{2})

s^{4} + \frac{41 s ^{3}}{5} + \frac{433 s ^{2}}{20} + \frac{209 s}{10} + 6

求解步骤

(s + 4) (s + \frac{1}{2}) (s + \frac{6}{5}) (s + \frac{5}{2})

展开

(s + 4) (s + \frac{1}{2}) (s + \frac{6}{5}) (s + \frac{5}{2}) : (s^{2} + \frac{9}{2} s + 2) (s + \frac{6}{5}) (s + \frac{5}{2})

= (s^{2} + \frac{9}{2} s + 2) (s + \frac{6}{5}) (s + \frac{5}{2})

Apply FOIL method

(s + \frac{6}{5}) (s + \frac{5}{2}) : s^{2} + \frac{37 s}{10} + 3

= (s^{2} + \frac{9}{2} s + 2) (s^{2} + \frac{37 s}{10} + 3)

打开括号

= s^{2} s^{2} + s^{2} \frac{37 s}{10} + s^{2} \cdot 3 + \frac{9}{2} s s^{2} + \frac{9}{2} s \frac{37 s}{10} + \frac{9}{2} s \cdot 3 + 2 s^{2} + 2 \cdot \frac{37 s}{10} + 2 \cdot 3

化简

s^{2} s^{2} + s^{2} \frac{37 s}{10} + s^{2} \cdot 3 + \frac{9}{2} s s^{2} + \frac{9}{2} s \frac{37 s}{10} + \frac{9}{2} s \cdot 3 + 2 s^{2} + 2 \cdot \frac{37 s}{10} + 2 \cdot 3 : s^{4} + \frac{41 s ^{3}}{5} + \frac{433 s ^{2}}{20} + \frac{209 s}{10} + 6

= s^{4} + \frac{41 s ^{3}}{5} + \frac{433 s ^{2}}{20} + \frac{209 s}{10} + 6

e x p an d (e^{2 x} - 5 e^{x} + 6 = 1) e^{x}

e x p an d \frac{( x ^{2} + 1 ) ( x ^{2} - x + 1 )}{x ( x ^{2} + 2 )}

e x p an d \frac{s ^{3} ( 5 t ^{2} - 6 t + 3 H ( t ) - 3 e ^{- 2 t} )}{3 ( s + 2 )}

e x p an d 2 (π - 2)

s im pl i f y 7 (tan^{2} (θ) - 1 + cot^{4} (θ))