erweitern (X+XY^')[Y+XZ(Y+XZ)+Y^']

Lösung

erweitern

(X + X Y^{^{'}}) [Y + XZ (Y + XZ) + Y^{^{'}}]

X Y + X^{2} Y Z + X^{3} Z^{2} + X Y^{'} + X Y^{1 +'} + X^{2} Z Y^{1 +'} + X^{3} Z^{2} Y^{'} + X Y^{2'}

Schritte zur Lösung

(X + X Y^{^{'}}) [Y + XZ (Y + XZ) + Y^{^{'}}]

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = [Y + XZ (Y + XZ) + Y^{^{'}}], b = X, c = X Y^{^{'}}

= [Y + XZ (Y + XZ) + Y^{^{^{'}}}] X + [Y + XZ (Y + XZ) + Y^{^{^{'}}}] X Y^{^{^{'}}}

= X [Y + XZ (Y + XZ) + Y^{^{^{'}}}] + X Y^{^{^{'}}} [Y + XZ (Y + XZ) + Y^{^{^{'}}}]

Vereinfache

X [Y + XZ (Y + XZ) + Y^{^{'}}] + X Y^{^{'}} [Y + XZ (Y + XZ) + Y^{^{'}}] : X Y + X^{2} Y Z + X^{3} Z^{2} + X Y^{^{'}} + X Y^{1 +^{'}} + X^{2} Z Y^{1 +^{'}} + X^{3} Z^{2} Y^{^{'}} + X Y^{2^{'}}

= X Y + X^{2} Y Z + X^{3} Z^{2} + X Y^{^{'}} + X Y^{1 +^{'}} + X^{2} Z Y^{1 +^{'}} + X^{3} Z^{2} Y^{^{'}} + X Y^{2^{'}}

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

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

e x p an d (x - 1) e

e x p an d \frac{1}{( x ^{5} + 4 x ) ^{3} - 6}

e x p an d \frac{- 10 - x ( x + 3 )}{- 15 - x ( x + 8 )}