化简 ((8u)/5+(3v^2)/8)((8u)/5-(3v^2)/8)

解答

化简

(\frac{8 u}{5} + \frac{3 v ^{2}}{8}) (\frac{8 u}{5} - \frac{3 v ^{2}}{8})

\frac{( 64 u + 15 v ^{2} ) ( 64 u - 15 v ^{2} )}{1600}

求解步骤

(\frac{8 u}{5} + \frac{3 v ^{2}}{8}) (\frac{8 u}{5} - \frac{3 v ^{2}}{8})

合并

\frac{8 u}{5} + \frac{3 v ^{2}}{8} : \frac{64 u + 15 v ^{2}}{40}

= \frac{64 u + 15 v ^{2}}{40} (\frac{8 u}{5} - \frac{3 v ^{2}}{8})

使用分式法则:

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

= \frac{( 64 u + 15 v ^{2} ) ( \frac{8 u}{5} - \frac{3 v ^{2}}{8} )}{40}

化简

(64 u + 15 v^{2}) (\frac{8 u}{5} - \frac{3 v ^{2}}{8}) : \frac{( 64 u + 15 v ^{2} ) ( 64 u - 15 v ^{2} )}{40}

= \frac{\frac{( 64 u + 15 v ^{2} ) ( 64 u - 15 v ^{2} )}{40}}{40}

使用分式法则:

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

= \frac{( 64 u + 15 v ^{2} ) ( 64 u - 15 v ^{2} )}{40 \cdot 40}

数字相乘:

40 \cdot 40 = 1600

= \frac{( 64 u + 15 v ^{2} ) ( 64 u - 15 v ^{2} )}{1600}

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