erweitern ((t+c)^2)/(10000pi^2)

Lösung

erweitern

\frac{( t + c ) ^{2}}{10000 π ^{2}}

\frac{t ^{2}}{10000 π ^{2}} + \frac{c t}{5000 π ^{2}} + \frac{c ^{2}}{10000 π ^{2}}

Schritte zur Lösung

\frac{( t + c ) ^{2}}{10000 π ^{2}}

(t + c)^{2} = t^{2} + 2 c t + c^{2}

= \frac{t ^{2} + 2 c t + c ^{2}}{10000 π ^{2}}

Wende Bruchregel an:

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

\frac{t ^{2} + 2 t c + c ^{2}}{10000 π ^{2}} = \frac{t ^{2}}{10000 π ^{2}} + \frac{2 t c}{10000 π ^{2}} + \frac{c ^{2}}{10000 π ^{2}}

= \frac{t ^{2}}{10000 π ^{2}} + \frac{2 c t}{10000 π ^{2}} + \frac{c ^{2}}{10000 π ^{2}}

Streiche

\frac{2 t c}{10000 π ^{2}} : \frac{c t}{5000 π ^{2}}

= \frac{t ^{2}}{10000 π ^{2}} + \frac{c t}{5000 π ^{2}} + \frac{c ^{2}}{10000 π ^{2}}

e x p an d \frac{5}{( 1 - x ) ^{2}}

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

e x p an d \frac{25 ( 95 + 8705 )}{2}

e x p an d (3 x^{2} + 2 x + 1)^{5}

e x p an d - 4 (- y + 5 z = 7)