erweitern (x^2+y^2)(e^{xy}xy+e^{xy})

Lösung

erweitern

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

e^{x y} x^{3} y + e^{x y} x^{2} + e^{x y} x y^{3} + e^{x y} y^{2}

Schritte zur Lösung

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

Wende Ausklammerungsregel an (VANI):

(a + b) (c + d) = a c + a d + b c + b d

a = x^{2}, b = y^{2}, c = e^{x y} x y, d = e^{x y}

= x^{2} e^{x y} x y + x^{2} e^{x y} + y^{2} e^{x y} x y + y^{2} e^{x y}

= e^{x y} x^{2} x y + e^{x y} x^{2} + e^{x y} x y^{2} y + e^{x y} y^{2}

Vereinfache

e^{x y} x^{2} x y + e^{x y} x^{2} + e^{x y} x y^{2} y + e^{x y} y^{2} : e^{x y} x^{3} y + e^{x y} x^{2} + e^{x y} x y^{3} + e^{x y} y^{2}

= e^{x y} x^{3} y + e^{x y} x^{2} + e^{x y} x y^{3} + e^{x y} y^{2}

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

e x p an d \frac{64}{( s ^{2} + 1 ) ( s + 8 )}

e x p an d 2 (m + 2 = 22)

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

e x p an d \frac{6 x - 8}{( 3 x + 4 ) ^{2}}