展开 ((1125b^2+256a^3)^3)/(125000000)

解答

展开

\frac{( 1125 b ^{2} + 256 a ^{3} ) ^{3}}{125000000}

\frac{112 5 ^{3} b ^{6}}{125000000} + \frac{972 b ^{4} a ^{3}}{125} + \frac{27648 b ^{2} a ^{6}}{15625} + \frac{262144 a ^{9}}{1953125}

求解步骤

\frac{( 1125 b ^{2} + 256 a ^{3} ) ^{3}}{125000000}

(1125 b^{2} + 256 a^{3})^{3} = 112 5^{3} b^{6} + 972000000 b^{4} a^{3} + 221184000 b^{2} a^{6} + 16777216 a^{9}

= \frac{112 5 ^{3} b ^{6} + 972000000 b ^{4} a ^{3} + 221184000 b ^{2} a ^{6} + 16777216 a ^{9}}{125000000}

使用分式法则:

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

\frac{112 5 ^{3} b ^{6} + 972000000 b ^{4} a ^{3} + 221184000 b ^{2} a ^{6} + 16777216 a ^{9}}{125000000} = \frac{112 5 ^{3} b ^{6}}{125000000} + \frac{972000000 b ^{4} a ^{3}}{125000000} + \frac{221184000 b ^{2} a ^{6}}{125000000} + \frac{16777216 a ^{9}}{125000000}

= \frac{112 5 ^{3} b ^{6}}{125000000} + \frac{972000000 b ^{4} a ^{3}}{125000000} + \frac{221184000 b ^{2} a ^{6}}{125000000} + \frac{16777216 a ^{9}}{125000000}

消掉

\frac{972000000 b ^{4} a ^{3}}{125000000} : \frac{972 b ^{4} a ^{3}}{125}

= \frac{112 5 ^{3} b ^{6}}{125000000} + \frac{972 b ^{4} a ^{3}}{125} + \frac{221184000 b ^{2} a ^{6}}{125000000} + \frac{16777216 a ^{9}}{125000000}

消掉

\frac{221184000 b ^{2} a ^{6}}{125000000} : \frac{27648 b ^{2} a ^{6}}{15625}

= \frac{112 5 ^{3} b ^{6}}{125000000} + \frac{972 b ^{4} a ^{3}}{125} + \frac{27648 b ^{2} a ^{6}}{15625} + \frac{16777216 a ^{9}}{125000000}

消掉

\frac{16777216 a ^{9}}{125000000} : \frac{262144 a ^{9}}{1953125}

= \frac{112 5 ^{3} b ^{6}}{125000000} + \frac{972 b ^{4} a ^{3}}{125} + \frac{27648 b ^{2} a ^{6}}{15625} + \frac{262144 a ^{9}}{1953125}

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