展开 (4(x+2)^3)/((s+1)(s-1)^2)

解答

展开

\frac{4 ( x + 2 ) ^{3}}{( s + 1 ) ( s - 1 ) ^{2}}

\frac{4 x ^{3} + 24 x ^{2} + 48 x + 32}{s ^{3} - s ^{2} - s + 1}

求解步骤

\frac{4 ( x + 2 ) ^{3}}{( s + 1 ) ( s - 1 ) ^{2}}

(s - 1)^{2} = s^{2} - 2 s + 1

= \frac{4 ( x + 2 ) ^{3}}{( s + 1 ) ( s ^{2} - 2 s + 1 )}

(x + 2)^{3} = x^{3} + 6 x^{2} + 12 x + 8

= \frac{4 ( x ^{3} + 6 x ^{2} + 12 x + 8 )}{( s + 1 ) ( s ^{2} - 2 s + 1 )}

乘开

(s + 1) (s^{2} - 2 s + 1) : s^{3} - s^{2} - s + 1

= \frac{4 ( x ^{3} + 6 x ^{2} + 12 x + 8 )}{s ^{3} - s ^{2} - s + 1}

乘开

4 (x^{3} + 6 x^{2} + 12 x + 8) : 4 x^{3} + 24 x^{2} + 48 x + 32

= \frac{4 x ^{3} + 24 x ^{2} + 48 x + 32}{s ^{3} - s ^{2} - s + 1}

e x p an d \frac{( 6 x - 1 ) ^{2}}{4}

e x p an d (- 9 + 3) (4 - 7)

e x p an d - 2 x^{\frac{7}{2}} (x^{2} + 1)

e x p an d (e^{x} + 1) (\frac{e ^{2 x}}{4 ( e ^{x} + 1 )} + 1)

e x p an d \frac{2 ( cos ( θ ) + sin ( θ ) )}{sin ( 2 θ ) + cos ( 2 θ ) + 1}