erweitern 5(sqrt(3/7)u-sqrt(3/13)v^2)^2

Lösung

erweitern

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}

Schritte zur Lösung

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

Wende Formel für perfekte quadratische Gleichungen an:

(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}

Vereinfache

(\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}

Wende Bruchregel an:

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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s im pl i f y (x - 1 + 3) (x + 1 + 3)