erweitern 7(2/(sqrt(13))x+3/(sqrt(13))y)^2

Lösung

erweitern

7 (\frac{2}{13} x + \frac{3}{13} y)^{2}

\frac{7 ( 4 x ^{2} + 12 x y + 9 y ^{2} )}{13}

Schritte zur Lösung

7 (\frac{2}{13} x + \frac{3}{13} y)^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

(\frac{2}{13} x + \frac{3}{13} y)^{2} = (\frac{2}{13} x)^{2} + 2 \cdot \frac{2}{13} x \frac{3}{13} y + (\frac{3}{13} y)^{2}

= 7 ((\frac{2}{13} x)^{2} + 2 \cdot \frac{2}{13} x \frac{3}{13} y + (\frac{3}{13} y)^{2})

Vereinfache

(\frac{2}{13} x)^{2} + 2 \cdot \frac{2}{13} x \frac{3}{13} y + (\frac{3}{13} y)^{2} : \frac{4 x ^{2} + 12 x y + 9 y ^{2}}{13}

= 7 \cdot \frac{4 x ^{2} + 12 x y + 9 y ^{2}}{13}

Wende Bruchregel an:

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

= \frac{7 ( 4 x ^{2} + 12 x y + 9 y ^{2} )}{13}

e x p an d \frac{1}{s ^{2} ( s + 1 ) ^{2}}

e x p an d (1 + ln (x)) (- e + 2 x - x ln (x))

e x p an d (2 + 5) (2 + 5)

e x p an d 1 + x + y (- 1 - y^{'} (x))

e x p an d (cos^{2} (v) + u (sin^{2} (v)))^{2}