erweitern ((-10+x^2+y^2)^2)/4

Lösung

erweitern

\frac{( - 10 + x ^{2} + y ^{2} ) ^{2}}{4}

\frac{x ^{2} y ^{2}}{2} - 5 x^{2} + \frac{x ^{4}}{4} - 5 y^{2} + \frac{y ^{4}}{4} + 25

Schritte zur Lösung

\frac{( - 10 + x ^{2} + y ^{2} ) ^{2}}{4}

(- 10 + x^{2} + y^{2})^{2} = 2 x^{2} y^{2} - 20 x^{2} + x^{4} - 20 y^{2} + y^{4} + 100

= \frac{2 x ^{2} y ^{2} - 20 x ^{2} + x ^{4} - 20 y ^{2} + y ^{4} + 100}{4}

Wende Bruchregel an:

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

\frac{2 x ^{2} y ^{2} - 20 x ^{2} + x ^{4} - 20 y ^{2} + y ^{4} + 100}{4} = \frac{2 x ^{2} y ^{2}}{4} - \frac{20 x ^{2}}{4} + \frac{x ^{4}}{4} - \frac{20 y ^{2}}{4} + \frac{y ^{4}}{4} + \frac{100}{4}

= \frac{2 x ^{2} y ^{2}}{4} - \frac{20 x ^{2}}{4} + \frac{x ^{4}}{4} - \frac{20 y ^{2}}{4} + \frac{y ^{4}}{4} + \frac{100}{4}

\frac{2 x ^{2} y ^{2}}{4} = \frac{x ^{2} y ^{2}}{2}

\frac{20 x ^{2}}{4} = 5 x^{2}

\frac{20 y ^{2}}{4} = 5 y^{2}

\frac{100}{4} = 25

= \frac{x ^{2} y ^{2}}{2} - 5 x^{2} + \frac{x ^{4}}{4} - 5 y^{2} + \frac{y ^{4}}{4} + 25

e x p an d \frac{3 + 9 x}{( 1 + x ) ( 3 + 5 x )}

e x p an d (x - 2 - i) (x - 2 + i)

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

e x p an d 1 + \frac{( e ^{x} - e ^{- x} ) ^{2}}{4}

\frac{d}{d y} ((x) (x - y))