factorise 1+X+Y-Z+XY-YZ-ZX-XYZ
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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)
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