erweitern ((x-yz)^2)/4

Lösung

erweitern

\frac{( x - yz ) ^{2}}{4}

\frac{x ^{2}}{4} - \frac{x yz}{2} + \frac{y ^{2} z ^{2}}{4}

Schritte zur Lösung

\frac{( x - yz ) ^{2}}{4}

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

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

Wende Bruchregel an:

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

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

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

Streiche

\frac{2 x yz}{4} : \frac{x yz}{2}

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

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

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

e x p an d \frac{2 x + 4}{( x - 1 ) ( x + 3 )}

e x p an d 2.856 \cdot 1 0^{7}

e x p an d \frac{5 ( x - 10 )}{2}