展开 ((bs+a)^2)/(s^3)

解答

展开

\frac{( b s + a ) ^{2}}{s ^{3}}

\frac{b ^{2}}{s} + \frac{2 ba}{s ^{2}} + \frac{a ^{2}}{s ^{3}}

求解步骤

\frac{( b s + a ) ^{2}}{s ^{3}}

(b s + a)^{2} = b^{2} s^{2} + 2 ba s + a^{2}

= \frac{b ^{2} s ^{2} + 2 ba s + a ^{2}}{s ^{3}}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{b ^{2} s ^{2} + 2 ba s + a ^{2}}{s ^{3}} = \frac{b ^{2} s ^{2}}{s ^{3}} + \frac{2 ba s}{s ^{3}} + \frac{a ^{2}}{s ^{3}}

= \frac{b ^{2} s ^{2}}{s ^{3}} + \frac{2 ba s}{s ^{3}} + \frac{a ^{2}}{s ^{3}}

消掉

\frac{b ^{2} s ^{2}}{s ^{3}} : \frac{b ^{2}}{s}

= \frac{b ^{2}}{s} + \frac{2 ba s}{s ^{3}} + \frac{a ^{2}}{s ^{3}}

消掉

\frac{2 ba s}{s ^{3}} : \frac{2 ba}{s ^{2}}

= \frac{b ^{2}}{s} + \frac{2 ba}{s ^{2}} + \frac{a ^{2}}{s ^{3}}

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

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

e x p an d \frac{a}{( s + b ) ( s + a )}

e x p an d y (y^{2} + 1) d x

e x p an d \frac{2 ( 4 x - 14 ) ^{2}}{9}