$$\\(\sqrt{z})^4+4(\sqrt{z})^3(2z)+6(\sqrt{z})^2(2z)^2+4\sqrt{z}(2z)^3+(2z)^4+\\
(\sqrt{z})^4-4(\sqrt{z})^3(2z)+6(\sqrt{z})^2(2z)^2-4\sqrt{z}(2z)^3+(2z)^4\\\\
=2*(\sqrt{z})^4+2*6(\sqrt{z})^2(2z)^2+2*(2z)^4\\
=2*z^2+2*6z*4z^2+2*16z^4\\
=2z^2+48z^3+32z^4\\$$
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