$$6r_{1}^{2}r_{2}^{2}r_{3}^{2}-8r_{1}^{3}r_{2}^{3}+4r_{1}^{4}r_{3}^{4}$$
$2r_{1}^{2}\left(2r_{1}^{2}r_{3}^{4}-4r_{1}r_{2}^{3}+3r_{2}^{2}r_{3}^{2}\right)$
$$2\left(3r_{1}^{2}r_{2}^{2}r_{3}^{2}-4r_{1}^{3}r_{2}^{3}+2r_{1}^{4}r_{3}^{4}\right)$$
$$r_{1}^{2}\left(3r_{2}^{2}r_{3}^{2}-4r_{1}r_{2}^{3}+2r_{1}^{2}r_{3}^{4}\right)$$
$$2r_{1}^{2}\left(3r_{2}^{2}r_{3}^{2}-4r_{1}r_{2}^{3}+2r_{1}^{2}r_{3}^{4}\right)$$
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$4\left(r_{1}r_{3}\right)^{4}-8\left(r_{1}r_{2}\right)^{3}+6\left(r_{1}r_{2}r_{3}\right)^{2}$
