Which Expression will I Factorise?!

Algebra Level 3

{x2+y2=z2xy=z(x+y)2=80\begin{cases} x^{2}+y^{2}=z^{2} \\ xy=z \\ (x+y)^{2} = 80 \end{cases}

If the above system of equations holds true for some positive real numbers xx, yy, and zz, then find

z4(x3y+xy3z3).\large \frac{z^{4}}{\left(\frac{x^3y+xy^3}{z^3}\right)} .

Hint: Use factorization.

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