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

Lösung

erweitern

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

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

Schritte zur Lösung

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

(u + x)^{2} = u^{2} + 2 ux + x^{2}

= \frac{2 ( u ^{2} + 2 ux + x ^{2} )}{x ^{2}}

Multipliziere aus

2 (u^{2} + 2 ux + x^{2}) : 2 u^{2} + 4 ux + 2 x^{2}

= \frac{2 u ^{2} + 4 ux + 2 x ^{2}}{x ^{2}}

Wende Bruchregel an:

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

\frac{2 u ^{2} + 4 ux + 2 x ^{2}}{x ^{2}} = \frac{2 u ^{2}}{x ^{2}} + \frac{4 ux}{x ^{2}} + \frac{2 x ^{2}}{x ^{2}}

= \frac{2 u ^{2}}{x ^{2}} + \frac{4 ux}{x ^{2}} + \frac{2 x ^{2}}{x ^{2}}

Streiche

\frac{4 ux}{x ^{2}} : \frac{4 u}{x}

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

Streiche

\frac{2 x ^{2}}{x ^{2}} : 2

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

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

e x p an d 21 (\frac{4}{7})

e x p an d \frac{1}{5 \cdot ( c + 1 )}

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

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