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受欢迎的代数 >

展开 (((3-x))/9)^2

解答

展开

(\frac{( 3 - x )}{9})^{2}

解答

\frac{x ^{2}}{81} - \frac{2 x}{27} + \frac{1}{9}

求解步骤

(\frac{3 - x}{9})^{2}

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 3 - x ) ^{2}}{9 ^{2}}

(3 - x)^{2} = 9 - 6 x + x^{2}

= \frac{9 - 6 x + x ^{2}}{9 ^{2}}

9^{2} = 81

= \frac{9 - 6 x + x ^{2}}{81}

使用分式法则:

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

\frac{9 - 6 x + x ^{2}}{81} = \frac{9}{81} - \frac{6 x}{81} + \frac{x ^{2}}{81}

= \frac{9}{81} - \frac{6 x}{81} + \frac{x ^{2}}{81}

消掉

\frac{9}{81} : \frac{1}{9}

= \frac{1}{9} - \frac{6 x}{81} + \frac{x ^{2}}{81}

消掉

\frac{6 x}{81} : \frac{2 x}{27}

= \frac{1}{9} - \frac{2 x}{27} + \frac{x ^{2}}{81}

改写为标准形式

= \frac{x ^{2}}{81} - \frac{2 x}{27} + \frac{1}{9}

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