erweitern xe^{6xy}(ye^{6xy}+x)

Lösung

erweitern

x e^{6 x y} (y e^{6 x y} + x)

e^{12 x y} x y + e^{6 x y} x^{2}

Schritte zur Lösung

x e^{6 x y} (y e^{6 x y} + x)

= e^{6 x y} x (e^{6 x y} y + x)

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = x e^{6 x y}, b = y e^{6 x y}, c = x

= x e^{6 x y} y e^{6 x y} + x e^{6 x y} x

= e^{6 x y} e^{6 x y} x y + e^{6 x y} xx

Vereinfache

e^{6 x y} e^{6 x y} x y + e^{6 x y} xx : e^{12 x y} x y + e^{6 x y} x^{2}

= e^{12 x y} x y + e^{6 x y} x^{2}

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

e x p an d \frac{x ^{2} ( 9 - x ^{2} )}{( 3 - x ^{2} ) ^{2}}

e x p an d a cos (ω t - k x) + a cos (ω t - k (x + δ x))

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

e x p an d \frac{k ( s + 1 )}{s ^{2} ( s + 10 ) ( s + 100 )}