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受欢迎的代数 >

展开 ((u+2a)^3)/u

解答

展开

\frac{( u + 2 a ) ^{3}}{u}

解答

u^{2} + 6 u a + 12 a^{2} + \frac{8 a ^{3}}{u}

求解步骤

\frac{( u + 2 a ) ^{3}}{u}

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

= \frac{u ^{3} + 6 u ^{2} a + 12 u a ^{2} + 8 a ^{3}}{u}

使用分式法则:

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

\frac{u ^{3} + 6 u ^{2} a + 12 u a ^{2} + 8 a ^{3}}{u} = \frac{u ^{3}}{u} + \frac{6 u ^{2} a}{u} + \frac{12 u a ^{2}}{u} + \frac{8 a ^{3}}{u}

= \frac{u ^{3}}{u} + \frac{6 u ^{2} a}{u} + \frac{12 u a ^{2}}{u} + \frac{8 a ^{3}}{u}

消掉

\frac{u ^{3}}{u} : u^{2}

= u^{2} + \frac{6 u ^{2} a}{u} + \frac{12 u a ^{2}}{u} + \frac{8 a ^{3}}{u}

消掉

\frac{6 u ^{2} a}{u} : 6 u a

= u^{2} + 6 u a + \frac{12 u a ^{2}}{u} + \frac{8 a ^{3}}{u}

消掉

\frac{12 u a ^{2}}{u} : 12 a^{2}

= u^{2} + 6 u a + 12 a^{2} + \frac{8 a ^{3}}{u}

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