展开 ((3h+k-3)/(sqrt(10)))^2

解答

展开

(\frac{3 h + k - 3}{10})^{2}

\frac{3 hk}{5} + \frac{9 h ^{2}}{10} - \frac{9 h}{5} + \frac{k ^{2}}{10} - \frac{3 k}{5} + \frac{9}{10}

求解步骤

(\frac{3 h + k - 3}{10})^{2}

使用指数法则:

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

= \frac{( 3 h + k - 3 ) ^{2}}{( 10 ) ^{2}}

(10)^{2} : 10

= \frac{( 3 h + k - 3 ) ^{2}}{10}

(3 h + k - 3)^{2} = 6 hk + 9 h^{2} - 18 h + k^{2} - 6 k + 9

= \frac{6 hk + 9 h ^{2} - 18 h + k ^{2} - 6 k + 9}{10}

使用分式法则:

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

\frac{6 hk + 9 h ^{2} - 18 h + k ^{2} - 6 k + 9}{10} = \frac{6 hk}{10} + \frac{9 h ^{2}}{10} - \frac{18 h}{10} + \frac{k ^{2}}{10} - \frac{6 k}{10} + \frac{9}{10}

= \frac{6 hk}{10} + \frac{9 h ^{2}}{10} - \frac{18 h}{10} + \frac{k ^{2}}{10} - \frac{6 k}{10} + \frac{9}{10}

消掉

\frac{6 hk}{10} : \frac{3 hk}{5}

= \frac{3 hk}{5} + \frac{9 h ^{2}}{10} - \frac{18 h}{10} + \frac{k ^{2}}{10} - \frac{6 k}{10} + \frac{9}{10}

消掉

\frac{18 h}{10} : \frac{9 h}{5}

= \frac{3 hk}{5} + \frac{9 h ^{2}}{10} - \frac{9 h}{5} + \frac{k ^{2}}{10} - \frac{6 k}{10} + \frac{9}{10}

消掉

\frac{6 k}{10} : \frac{3 k}{5}

= \frac{3 hk}{5} + \frac{9 h ^{2}}{10} - \frac{9 h}{5} + \frac{k ^{2}}{10} - \frac{3 k}{5} + \frac{9}{10}

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