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

Lösung

erweitern

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

x^{3} + 3 x + \frac{3}{x} + \frac{1}{x ^{3}}

Schritte zur Lösung

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

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = (x + \frac{1}{x})^{2}, b = x, c = \frac{1}{x}

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

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

Vereinfache

x (x + \frac{1}{x})^{2} + \frac{1}{x} (x + \frac{1}{x})^{2} : x^{3} + 3 x + \frac{3}{x} + \frac{1}{x ^{3}}

= x^{3} + 3 x + \frac{3}{x} + \frac{1}{x ^{3}}

\frac{d ^{2}}{d x ^{2}} ((x) (5 \cdot x^{3} - 2 \cdot x^{2} + 2 \cdot x))

e x p an d \frac{( 1 - j ^{2} ) e ^{(0.5 - j^{1.047})}}{( 3 - j ^{4} )}

e x p an d \frac{2}{( x - 5 ) ^{6}}

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

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