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expand 1/12*((x+y+z)^6 + 2(x^6+y^6+z^6) + 2(x^3+y^3+z^3)^2 + 4(x^2+y^2+z^2)^3 + 3(x+y+z)^2(x^2+y^2+z^2)^2)
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