erweitern ((x-y)^2)/(4x^6)

Lösung

erweitern

\frac{( x - y ) ^{2}}{4 x ^{6}}

\frac{1}{4 x ^{4}} - \frac{y}{2 x ^{5}} + \frac{y ^{2}}{4 x ^{6}}

Schritte zur Lösung

\frac{( x - y ) ^{2}}{4 x ^{6}}

(x - y)^{2} = x^{2} - 2 x y + y^{2}

= \frac{x ^{2} - 2 x y + y ^{2}}{4 x ^{6}}

Wende Bruchregel an:

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

\frac{x ^{2} - 2 x y + y ^{2}}{4 x ^{6}} = \frac{x ^{2}}{4 x ^{6}} - \frac{2 x y}{4 x ^{6}} + \frac{y ^{2}}{4 x ^{6}}

= \frac{x ^{2}}{4 x ^{6}} - \frac{2 x y}{4 x ^{6}} + \frac{y ^{2}}{4 x ^{6}}

Streiche

\frac{x ^{2}}{4 x ^{6}} : \frac{1}{4 x ^{4}}

= \frac{1}{4 x ^{4}} - \frac{2 x y}{4 x ^{6}} + \frac{y ^{2}}{4 x ^{6}}

Streiche

\frac{2 x y}{4 x ^{6}} : \frac{y}{2 x ^{5}}

= \frac{1}{4 x ^{4}} - \frac{y}{2 x ^{5}} + \frac{y ^{2}}{4 x ^{6}}

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

e x p an d π (\frac{250}{3} - 326)

s im pl i f y \frac{( a sin ( θ ) - a ) ^{2}}{a} + a

e x p an d \frac{( x - 4 ) ^{2}}{25}

e x p an d \frac{( n + 2 ) ( - 11 n + 15 )}{2}