erweitern (1+(2x)/n)^2

Lösung

erweitern

(1 + \frac{2 x}{n})^{2}

\frac{n ^{2} + 4 x n + 4 x ^{2}}{n ^{2}}

Schritte zur Lösung

(1 + \frac{2 x}{n})^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

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

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

Vereinfache

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

= \frac{n ^{2} + 4 x n + 4 x ^{2}}{n ^{2}}

e x p an d (1 + \frac{2}{3} x)^{7} (3 + 7 x)^{2}

e x p an d (x^{3} + 3 x + 1)^{6}

e x p an d \frac{5 x}{( 2 x + 1 ) ( x - 3 )}

e x p an d (cos (2 x) - e^{x}) (x^{2} + 1 - cos (x))

e x p an d A (2, 3, 4) y B (8, - 2, 3)