Question

1+ x + y - z + xy - yz - zx - xyz​

Answer 1

Answer: 55

Step-by-step explanation:

Answer 2

Answer:

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Step-by-step explanation:

The given expression is 1+X+Y-Z+XY-YZ-ZX-XYZ.

Gathering common terms

1+X+Y-Z+XY-YZ-ZX-XYZ=1+X+Y-YZ-ZX-Z+XY-XYZ\\
1+X+Y-Z+XY-YZ-ZX-XYZ=1-Z+X+Y-Z(Y+X)+XY-XYZ\\
1+X+Y-Z+XY-YZ-ZX-XYZ=1-Z+(X+Y)-Z(Y+X)+(XY-XYZ)\\
1+X+Y-Z+XY-YZ-ZX-XYZ=(1-Z)+(X+Y)(1-Z)+XY(1-Z)\\

Further simplifying,

1+X+Y-Z+XY-YZ-ZX-XYZ=(1-Z)[1+(X+Y)+XY]\\
1+X+Y-Z+XY-YZ-ZX-XYZ=(1-Z)(1+X)(1+Y)\\

Thus the final factorized expression is

1+X+Y-Z+XY-YZ-ZX-XYZ=(1+X)(1+Y)(1-Z)