展开 7(sqrt(3/5)u-sqrt(3/23)v)^2

解答

展开

7 (\frac{3}{5} u - \frac{3}{23} v)^{2}

\frac{7 ( - 230 \frac{3}{5} \frac{3}{23} uv + 69 u ^{2} + 15 v ^{2} )}{115}

求解步骤

7 (\frac{3}{5} u - \frac{3}{23} v)^{2}

使用完全平方公式:

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

(\frac{3}{5} u - \frac{3}{23} v)^{2} = (\frac{3}{5} u)^{2} - 2 \frac{3}{5} u \frac{3}{23} v + (\frac{3}{23} v)^{2}

= 7 (\frac{3}{5} u)^{2} - 2 \frac{3}{5} u \frac{3}{23} v + (\frac{3}{23} v)^{2}

化简

(\frac{3}{5} u)^{2} - 2 \frac{3}{5} u \frac{3}{23} v + (\frac{3}{23} v)^{2} : \frac{- 230 \frac{3}{5} \frac{3}{23} uv + 69 u ^{2} + 15 v ^{2}}{115}

= 7 \cdot \frac{- 230 \frac{3}{5} \frac{3}{23} uv + 69 u ^{2} + 15 v ^{2}}{115}

使用分式法则:

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

= \frac{7 ( - 230 \frac{3}{5} \frac{3}{23} uv + 69 u ^{2} + 15 v ^{2} )}{115}

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