erweitern (y^2+x^2)/((y+x)^2(x-y)^2)

Lösung

erweitern

\frac{y ^{2} + x ^{2}}{( y + x ) ^{2} ( x - y ) ^{2}}

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

Schritte zur Lösung

\frac{y ^{2} + x ^{2}}{( y + x ) ^{2} ( x - y ) ^{2}}

(y + x)^{2} = y^{2} + 2 y x + x^{2}

= \frac{y ^{2} + x ^{2}}{( y ^{2} + 2 y x + x ^{2} ) ( x - y ) ^{2}}

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

= \frac{y ^{2} + x ^{2}}{( y ^{2} + 2 y x + x ^{2} ) ( y ^{2} - 2 y x + x ^{2} )}

Multipliziere aus

(y^{2} + 2 y x + x^{2}) (x^{2} - 2 x y + y^{2}) : y^{4} - 2 y^{2} x^{2} + x^{4}

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

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

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

e x p an d 4 (y^{4} + 3 y^{2}) + 1

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

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