erweitern 5(1/(sqrt(5))x+2/(sqrt(5))y)^2

Lösung

erweitern

5 (\frac{1}{5} x + \frac{2}{5} y)^{2}

x^{2} + 4 x y + 4 y^{2}

Schritte zur Lösung

5 (\frac{1}{5} x + \frac{2}{5} y)^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

(\frac{1}{5} x + \frac{2}{5} y)^{2} = (\frac{1}{5} x)^{2} + 2 \cdot \frac{1}{5} x \frac{2}{5} y + (\frac{2}{5} y)^{2}

= 5 ((\frac{1}{5} x)^{2} + 2 \cdot \frac{1}{5} x \frac{2}{5} y + (\frac{2}{5} y)^{2})

Vereinfache

(\frac{1}{5} x)^{2} + 2 \cdot \frac{1}{5} x \frac{2}{5} y + (\frac{2}{5} y)^{2} : \frac{x ^{2} + 4 x y + 4 y ^{2}}{5}

= 5 \cdot \frac{x ^{2} + 4 x y + 4 y ^{2}}{5}

kürze gemeinsame Faktoren über Kreuz:

5

= x^{2} + 4 x y + 4 y^{2}

e x p an d (x - \frac{11 π}{2}) (tan (\frac{x}{11}))

e x p an d (1 - x) (1 - e^{- t})

e x p an d (sin (t) + t cos (t)) \cdot (2 cos (t) - t sin (t))

e x p an d (y - 3 x^{2}) d x

e x p an d \frac{\frac{4}{3}}{,} (\frac{1}{8} + \frac{1}{12} B i g) \frac{34}{( 81 + 121 )}