erweitern (5x^3zb+7d^5e^7)^2

Lösung

erweitern

(5 x^{3} z b + 7 d^{5} e^{7})^{2}

25 b^{2} x^{6} z^{2} + 70 e^{7} b d^{5} x^{3} z + 49 e^{14} d^{10}

Schritte zur Lösung

(5 x^{3} z b + 7 d^{5} e^{7})^{2}

= (5 b x^{3} z + 7 e^{7} d^{5})^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

a = 5 x^{3} z b, b = 7 d^{5} e^{7}

= (5 x^{3} z b)^{2} + 2 \cdot 5 x^{3} z b \cdot 7 d^{5} e^{7} + (7 d^{5} e^{7})^{2}

Vereinfache

(5 x^{3} z b)^{2} + 2 \cdot 5 x^{3} z b \cdot 7 d^{5} e^{7} + (7 d^{5} e^{7})^{2} : 25 b^{2} x^{6} z^{2} + 70 e^{7} b d^{5} x^{3} z + 49 e^{14} d^{10}

= 25 b^{2} x^{6} z^{2} + 70 e^{7} b d^{5} x^{3} z + 49 e^{14} d^{10}

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

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

s im pl i f y (x - \frac{3}{4}) (x + 2)

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

e x p an d \frac{d}{d x} ((x^{2} - a) e^{x}) + b x