xyz + xz + yz + x + y + z + xy + 1
= ( xyz + xy ) + ( xz + yz ) + ( x + y) + ( z + 1 )
= xy ( z + 1 ) + z ( x + y ) + ( x+ y) + (z + 1 )
= ( xy + 1 )(z-1) + ( x+ y)(z + 1 )
= (z + 1 )(xy + x + y + 1 )
xyz + xz + yz + x + y + z + xy + 1
= ( xyz + xy ) + ( xz + yz ) + ( x + y) + ( z + 1 )
= xy ( z + 1 ) + z ( x + y ) + ( x+ y) + (z + 1 )
= ( xy + 1 )(z-1) + ( x+ y)(z + 1 )
= (z + 1 )(xy + x + y + 1 )
=(z + 1)[ x.(y+1)+(y+1)]
=(z+1)(y+1)(x+1)