erweitern (-3a^2x(a-x)^2-3xz^2(a-x)^2)/2

Lösung

erweitern

\frac{- 3 a ^{2} x ( a - x ) ^{2} - 3 x z ^{2} ( a - x ) ^{2}}{2}

- \frac{3 a ^{4} x}{2} + 3 a^{3} x^{2} - \frac{3 a ^{2} x ^{3}}{2} - \frac{3 a ^{2} x z ^{2}}{2} + 3 a x^{2} z^{2} - \frac{3 x ^{3} z ^{2}}{2}

Schritte zur Lösung

\frac{- 3 a ^{2} x ( a - x ) ^{2} - 3 x z ^{2} ( a - x ) ^{2}}{2}

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

= \frac{- 3 a ^{2} x ( x ^{2} - 2 a x + a ^{2} ) - 3 x z ^{2} ( - x + a ) ^{2}}{2}

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

= \frac{- 3 a ^{2} x ( x ^{2} - 2 a x + a ^{2} ) - 3 x z ^{2} ( x ^{2} - 2 a x + a ^{2} )}{2}

Multipliziere aus

- 3 a^{2} x (a^{2} - 2 a x + x^{2}) - 3 x z^{2} (a^{2} - 2 a x + x^{2}) : - 3 a^{4} x + 6 a^{3} x^{2} - 3 a^{2} x^{3} - 3 a^{2} x z^{2} + 6 a x^{2} z^{2} - 3 x^{3} z^{2}

= \frac{- 3 a ^{4} x + 6 a ^{3} x ^{2} - 3 a ^{2} x ^{3} - 3 a ^{2} x z ^{2} + 6 a x ^{2} z ^{2} - 3 x ^{3} z ^{2}}{2}

Wende Bruchregel an:

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

\frac{- 3 a ^{4} x + 6 a ^{3} x ^{2} - 3 a ^{2} x ^{3} - 3 a ^{2} x z ^{2} + 6 a x ^{2} z ^{2} - 3 x ^{3} z ^{2}}{2} = - \frac{3 a ^{4} x}{2} + \frac{6 a ^{3} x ^{2}}{2} - \frac{3 a ^{2} x ^{3}}{2} - \frac{3 a ^{2} x z ^{2}}{2} + \frac{6 a x ^{2} z ^{2}}{2} - \frac{3 x ^{3} z ^{2}}{2}

= - \frac{3 a ^{4} x}{2} + \frac{6 a ^{3} x ^{2}}{2} - \frac{3 a ^{2} x ^{3}}{2} - \frac{3 a ^{2} x z ^{2}}{2} + \frac{6 a x ^{2} z ^{2}}{2} - \frac{3 x ^{3} z ^{2}}{2}

Teile die Zahlen:

\frac{6}{2} = 3

= - \frac{3 a ^{4} x}{2} + 3 a^{3} x^{2} - \frac{3 a ^{2} x ^{3}}{2} - \frac{3 a ^{2} x z ^{2}}{2} + 3 a x^{2} z^{2} - \frac{3 x ^{3} z ^{2}}{2}

e x p an d π (- 128 ln (3) + \frac{808}{3})

e x p an d - \frac{2 x}{2 x + 3} + ln ∣ 2 x + 3 ∣ - \frac{3}{2 ( 2 x + 3 )}

e x p an d (\frac{x}{4} - \frac{2 x}{5} = \frac{x + 2}{20} - \frac{x + 1}{10}) \cdot 2

e x p an d (a - 4 a x)^{2} + (b + 2 b x)^{2}

e x p an d \frac{z}{( z + 9 ) ^{2}}