Add the product: x(x + y−r), y(x−y + r), z(x−y−z)

Here we have the expressions x(x + y-r),y(x-y + r) and z(x-y-z)

Using the distributive law x(x + y-r)

= x² + xy-xr,y(x-y + r)

= xy-y² + yr and

z(x-y-z) = xz-yz-z²

Now we add these terms (x² + xy-xr) + (xy-y² + yr) + (xz-yz-z²)

= x²-y²-z² + 2xy-xr + yr + xz-yz

Hence addition of the product of the above expressions is x²-y²-z² + 2xy-xr + yr + xz-yz.