erweitern ((10p^2-x^2)^2)/(4p^2)

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

Wende Bruchregel an:

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

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

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

Streiche

\frac{100 p ^{4}}{4 p ^{2}} : 25 p^{2}

= 25 p^{2} - \frac{20 p ^{2} x ^{2}}{4 p ^{2}} + \frac{x ^{4}}{4 p ^{2}}

Streiche

\frac{20 p ^{2} x ^{2}}{4 p ^{2}} : 5 x^{2}

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

e x p an d (t - π)^{2}

e x p an d \frac{3 \cdot ( x + 3 )}{x}

e x p an d (3 x - 2) (x ln (x) - x)

e x p an d \frac{( 80 - t ) ^{2}}{2}

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