化简 y^4((2x^2)/(y^2)+1)

解答

化简

y^{4} (\frac{2 x ^{2}}{y ^{2}} + 1)

y^{2} (y^{2} + 2 x^{2})

求解步骤

y^{4} (\frac{2 x ^{2}}{y ^{2}} + 1)

合并

\frac{2 x ^{2}}{y ^{2}} + 1 : \frac{y ^{2} + 2 x ^{2}}{y ^{2}}

= y^{4} \frac{y ^{2} + 2 x ^{2}}{y ^{2}}

使用分式法则:

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

= \frac{y ^{4} ( y ^{2} + 2 x ^{2} )}{y ^{2}}

使用指数法则:

a^{b + c} = a^{b} \cdot a^{c}

y^{4} = y^{2} y^{2}

= \frac{y ^{2} y ^{2} ( y ^{2} + 2 x ^{2} )}{y ^{2}}

约分:

y^{2}

= y^{2} (y^{2} + 2 x^{2})

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

s im pl i f y (x + i x^{2})^{2} - 2 (x + i x^{2}) (1 + 2 i x)

e x p an d \frac{2 - e ^{- 3 π s}}{s ( s ^{2} + 1 )}

e x p an d \frac{100 ( 0.02 x + 4 ) ^{3}}{x}

e x p an d (f \circ g) (2 x - 1) (- x^{2})