erweitern ((ba^2+bx^2-bxa)^2)/(a^4)

Lösung

erweitern

\frac{( b a ^{2} + b x ^{2} - b x a ) ^{2}}{a ^{4}}

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

Schritte zur Lösung

\frac{( b a ^{2} + b x ^{2} - b x a ) ^{2}}{a ^{4}}

(b a^{2} + b x^{2} - b x a)^{2} = b^{2} x^{4} - 2 b^{2} a x^{3} + 3 b^{2} a^{2} x^{2} - 2 b^{2} a^{3} x + b^{2} a^{4}

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

Wende Bruchregel an:

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

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

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

\frac{2 b ^{2} a x ^{3}}{a ^{4}} = \frac{2 b ^{2} x ^{3}}{a ^{3}}

\frac{3 b ^{2} a ^{2} x ^{2}}{a ^{4}} = \frac{3 b ^{2} x ^{2}}{a ^{2}}

\frac{2 b ^{2} a ^{3} x}{a ^{4}} = \frac{2 b ^{2} x}{a}

\frac{b ^{2} a ^{4}}{a ^{4}} = b^{2}

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

e x p an d (\frac{8 - x}{2})^{3}

e x p an d \frac{3}{4 ( 2 x + 7 ) ^{9}}

e x p an d (2 - 2 e^{t})^{3}

e x p an d \frac{1}{( y - 4 ) ^{(5)}}

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