展开 (a(b-c)^2)/d

解答

展开

\frac{a ( b - c ) ^{2}}{d}

\frac{a b ^{2}}{d} - \frac{2 ab c}{d} + \frac{a c ^{2}}{d}

求解步骤

\frac{a ( b - c ) ^{2}}{d}

(b - c)^{2} = b^{2} - 2 b c + c^{2}

= \frac{a ( b ^{2} - 2 b c + c ^{2} )}{d}

乘开

a (b^{2} - 2 b c + c^{2}) : a b^{2} - 2 ab c + a c^{2}

= \frac{a b ^{2} - 2 ab c + a c ^{2}}{d}

使用分式法则:

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

\frac{a b ^{2} - 2 ab c + a c ^{2}}{d} = \frac{a b ^{2}}{d} - \frac{2 ab c}{d} + \frac{a c ^{2}}{d}

= \frac{a b ^{2}}{d} - \frac{2 ab c}{d} + \frac{a c ^{2}}{d}

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