展开 ((3xa+b)^3)/(27a^3)

解答

展开

\frac{( 3 x a + b ) ^{3}}{27 a ^{3}}

x^{3} + \frac{b x ^{2}}{a} + \frac{b ^{2} x}{3 a ^{2}} + \frac{b ^{3}}{27 a ^{3}}

求解步骤

\frac{( 3 x a + b ) ^{3}}{27 a ^{3}}

(3 x a + b)^{3} = 27 a^{3} x^{3} + 27 a^{2} b x^{2} + 9 a b^{2} x + b^{3}

= \frac{27 a ^{3} x ^{3} + 27 a ^{2} b x ^{2} + 9 a b ^{2} x + b ^{3}}{27 a ^{3}}

使用分式法则:

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

\frac{27 a ^{3} x ^{3} + 27 a ^{2} b x ^{2} + 9 a b ^{2} x + b ^{3}}{27 a ^{3}} = \frac{27 a ^{3} x ^{3}}{27 a ^{3}} + \frac{27 a ^{2} b x ^{2}}{27 a ^{3}} + \frac{9 a b ^{2} x}{27 a ^{3}} + \frac{b ^{3}}{27 a ^{3}}

= \frac{27 a ^{3} x ^{3}}{27 a ^{3}} + \frac{27 a ^{2} b x ^{2}}{27 a ^{3}} + \frac{9 a b ^{2} x}{27 a ^{3}} + \frac{b ^{3}}{27 a ^{3}}

消掉

\frac{27 a ^{3} x ^{3}}{27 a ^{3}} : x^{3}

= x^{3} + \frac{27 a ^{2} b x ^{2}}{27 a ^{3}} + \frac{9 a b ^{2} x}{27 a ^{3}} + \frac{b ^{3}}{27 a ^{3}}

消掉

\frac{27 a ^{2} b x ^{2}}{27 a ^{3}} : \frac{b x ^{2}}{a}

= x^{3} + \frac{b x ^{2}}{a} + \frac{9 a b ^{2} x}{27 a ^{3}} + \frac{b ^{3}}{27 a ^{3}}

消掉

\frac{9 a b ^{2} x}{27 a ^{3}} : \frac{b ^{2} x}{3 a ^{2}}

= x^{3} + \frac{b x ^{2}}{a} + \frac{b ^{2} x}{3 a ^{2}} + \frac{b ^{3}}{27 a ^{3}}

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