Simplify Product of Sums

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Similar question to: Boolean Algebra - Product of Sums

I was given a truth table and asked to give the sums-of-products and the product-of-sums expressions.

I reduced the sums-of-products expression to this, which I believe is correct:

$$F(x,y,z) = xy + yz + xz$$

I have so far reduced my product-of-sums expression to this:

$$F(x,y,z) = (x+y+z)(x+y+z’)(x+y’+z)(x’+y+z)$$

but I can't figure out how to further reduce my product-of-sums, whilst still retaining the "product-of-sums" form and not converting back to "sums-of-products" form. If someone could show me how to further reduce the product-of-sums, I would be appreciative if you could explain which Boolean identity is being used at each stage of of the simplification (i.e. Distributive Law, DeMorgan's Law etc). Thanks!