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受欢迎的代数 >

展开 (36x(2x-y)^2)/(y^3)

解答

展开

\frac{36 x ( 2 x - y ) ^{2}}{y ^{3}}

解答

\frac{144 x ^{3}}{y ^{3}} - \frac{144 x ^{2}}{y ^{2}} + \frac{36 x}{y}

求解步骤

\frac{36 x ( 2 x - y ) ^{2}}{y ^{3}}

(2 x - y)^{2} = 4 x^{2} - 4 x y + y^{2}

= \frac{36 x ( 4 x ^{2} - 4 x y + y ^{2} )}{y ^{3}}

乘开

36 x (4 x^{2} - 4 x y + y^{2}) : 144 x^{3} - 144 x^{2} y + 36 x y^{2}

= \frac{144 x ^{3} - 144 x ^{2} y + 36 x y ^{2}}{y ^{3}}

使用分式法则:

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

\frac{144 x ^{3} - 144 x ^{2} y + 36 x y ^{2}}{y ^{3}} = \frac{144 x ^{3}}{y ^{3}} - \frac{144 x ^{2} y}{y ^{3}} + \frac{36 x y ^{2}}{y ^{3}}

= \frac{144 x ^{3}}{y ^{3}} - \frac{144 x ^{2} y}{y ^{3}} + \frac{36 x y ^{2}}{y ^{3}}

消掉

\frac{144 x ^{2} y}{y ^{3}} : \frac{144 x ^{2}}{y ^{2}}

= \frac{144 x ^{3}}{y ^{3}} - \frac{144 x ^{2}}{y ^{2}} + \frac{36 x y ^{2}}{y ^{3}}

消掉

\frac{36 x y ^{2}}{y ^{3}} : \frac{36 x}{y}

= \frac{144 x ^{3}}{y ^{3}} - \frac{144 x ^{2}}{y ^{2}} + \frac{36 x}{y}

流行的例子

展开 2Lx-3x^2

e x p an d 2 Lx - 3 x^{2}

展开 (5x+4)/((x+12)(x-12))

e x p an d \frac{5 x + 4}{( x + 12 ) ( x - 12 )}

展开 (s+7)/((s+2)(s-5))

e x p an d \frac{s + 7}{( s + 2 ) ( s - 5 )}

e x p an d c + 4

展开 (P(x-i)^2)/2

e x p an d \frac{P ( x - i ) ^{2}}{2}