展开 (X+XY^')[Y+XZ(Y+XZ)+Y^']

解答

展开

(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'}

求解步骤

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

使用分配律:

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^{^{^{'}}}]

化简

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^{'}}

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