展开 5(sqrt(3/7)u-sqrt(3/13)v^2)^2

解答

展开

5 (\frac{3}{7} u - \frac{3}{13} v^{2})^{2}

\frac{5 ( - 182 \frac{3}{7} \frac{3}{13} u v ^{2} + 39 u ^{2} + 21 v ^{4} )}{91}

求解步骤

5 (\frac{3}{7} u - \frac{3}{13} v^{2})^{2}

使用完全平方公式:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(\frac{3}{7} u - \frac{3}{13} v^{2})^{2} = (\frac{3}{7} u)^{2} - 2 \frac{3}{7} u \frac{3}{13} v^{2} + (\frac{3}{13} v^{2})^{2}

= 5 (\frac{3}{7} u)^{2} - 2 \frac{3}{7} u \frac{3}{13} v^{2} + (\frac{3}{13} v^{2})^{2}

化简

(\frac{3}{7} u)^{2} - 2 \frac{3}{7} u \frac{3}{13} v^{2} + (\frac{3}{13} v^{2})^{2} : \frac{- 182 \frac{3}{7} \frac{3}{13} u v ^{2} + 39 u ^{2} + 21 v ^{4}}{91}

= 5 \cdot \frac{- 182 \frac{3}{7} \frac{3}{13} u v ^{2} + 39 u ^{2} + 21 v ^{4}}{91}

使用分式法则:

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

= \frac{5 ( - 182 \frac{3}{7} \frac{3}{13} u v ^{2} + 39 u ^{2} + 21 v ^{4} )}{91}

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