erweitern (e^2-2ey+y^2)(e^2-2x+x^2)-(e^2-2x+x^2)r

Lösung

erweitern

(e^{2} - 2 ey + y^{2}) (e^{2} - 2 x + x^{2}) - (e^{2} - 2 x + x^{2}) r

e^{4} - 2 e^{2} x + e^{2} x^{2} - 2 e^{3} y + 4 ey x - 2 ey x^{2} + e^{2} y^{2} - 2 y^{2} x + y^{2} x^{2} - e^{2} r + 2 x r - x^{2} r

Schritte zur Lösung

(e^{2} - 2 ey + y^{2}) (e^{2} - 2 x + x^{2}) - (e^{2} - 2 x + x^{2}) r

= (e^{2} - 2 ey + y^{2}) (e^{2} - 2 x + x^{2}) - r (e^{2} - 2 x + x^{2})

Multipliziere aus

(e^{2} - 2 ey + y^{2}) (e^{2} - 2 x + x^{2}) : e^{4} - 2 e^{2} x + e^{2} x^{2} - 2 e^{3} y + 4 ey x - 2 ey x^{2} + e^{2} y^{2} - 2 y^{2} x + y^{2} x^{2}

= e^{4} - 2 e^{2} x + e^{2} x^{2} - 2 e^{3} y + 4 ey x - 2 ey x^{2} + e^{2} y^{2} - 2 y^{2} x + y^{2} x^{2} - (e^{2} - 2 x + x^{2}) r

Multipliziere aus

- r (e^{2} - 2 x + x^{2}) : - e^{2} r + 2 x r - x^{2} r

= e^{4} - 2 e^{2} x + e^{2} x^{2} - 2 e^{3} y + 4 ey x - 2 ey x^{2} + e^{2} y^{2} - 2 y^{2} x + y^{2} x^{2} - e^{2} r + 2 x r - x^{2} r

e x p an d \frac{4 n ^{3} + 15 n ^{2} + 11 n}{6}

e x p an d (1 - x) y^{''} (x) + x y

e x p an d \frac{x ^{2} + y ^{2} + z ^{2}}{2} - \frac{( x + y + z ) ^{2}}{6}

e x p an d \frac{sec ^{2} ( x )}{( 1 + tan ( x ) ) ^{3}}

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