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a guest Jun 15th, 2019 63 Never
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  1. Resultant[x^4 - 4*(a + b + c)*x^3 + 2*(3*(a + b + c)^2 - 4*(a*b + a*c + b*c))*x^2 - 4*((a + b + c)^3 - 4*(a + b + c)*(a*b + a*c + b*c) + 16*a*b*c)*x+ (4*(a*b + a*c + b*c) - (a + b + c)^2)^2, x^8 - 8*(d + e + f + g)*x^7 + 4*(7*(d + e + f + g)^2 - 4*(d*e + d*f + e*f + d*g + e*g + f*g))*x^6 - 8*(7*(d + e + f + g)^3 - 12*(d + e + f + g)*(d*e + d*f + e*f + d*g + e*g + f*g) + 16*(d*e*f + d*e*g + d*f*g + e*f*g))*x^5 + 2*(-1088*(d*e*f*g) + 35*(d + e + f + g)^4 - 120*(d + e + f + g)^2*(d*e + d*f + e*f + d*g + e*g + f*g) + 48*(d*e + d*f + e*f + d*g + e*g + f*g)^2 + 256*(d + e + f + g)*(d*e*f + d*e*g + d*f*g + e*f*g))*x^4 - 8*(-320*(d*e*f*g)*(d + e + f + g) + 7*(d + e + f + g)^5 -
  2.  40*(d + e + f + g)^3*(d*e + d*f + e*f + d*g + e*g + f*g) + 48*(d + e + f + g)*(d*e + d*f + e*f + d*g + e*g + f*g)^2 +
  3.  96*(d + e + f + g)^2*(d*e*f + d*e*g + d*f*g + e*f*g) - 128*(d*e + d*f + e*f + d*g + e*g + f*g)*(d*e*f + d*e*g + d*f*g + e*f*g))*x^3 + 4*(320*(d*e*f*g)*(d + e + f + g)^2 + 7*(d + e + f + g)^6 - 1792*(d*e*f*g)*(d*e + d*f + e*f + d*g + e*g + f*g) -
  4.  60*(d + e + f + g)^4*(d*e + d*f + e*f + d*g + e*g + f*g) + 144*(d + e + f + g)^2*(d*e + d*f + e*f + d*g + e*g + f*g)^2 -
  5.  64*(d*e + d*f + e*f + d*g + e*g + f*g)^3 + 128*(d + e + f + g)^3*(d*e*f + d*e*g + d*f*g + e*f*g) -
  6.  512*(d + e + f + g)*(d*e + d*f + e*f + d*g + e*g + f*g)*(d*e*f + d*e*g + d*f*g + e*f*g) + 1024*(d*e*f*g)^2)*x^2 - 8*(192*(d*e*f*g)*(d + e + f + g)^3 + (d + e + f + g)^8 - 768*(d*e*f*g)*(d + e + f + g)*(d*e + d*f + e*f + d*g + e*g + f*g) -
  7.  12*(d + e + f + g)^5*(d*e + d*f + e*f + d*g + e*g + f*g) + 48*(d + e + f + g)^3*(d*e + d*f + e*f + d*g + e*g + f*g)^2 -
  8.  64*(d + e + f + g)*(d*e + d*f + e*f + d*g + e*g + f*g)^3 + 1024*(d*e*f*g)*(d*e*f + d*e*g + d*f*g + e*f*g) +
  9.  16*(d + e + f + g)^4*(d*e*f + d*e*g + d*f*g + e*f*g) - 128*(d + e + f + g)^2*(d*e + d*f + e*f + d*g + e*g + f*g)*(d*e*f + d*e*g + d*f*g + e*f*g) +
  10.  256*(d*e + d*f + e*f + d*g + e*g + f*g)^2*(d*e*f + d*e*g + d*f*g + e*f*g))*x + (((d + e + f + g)^2 - 4*(d*e + d*f + e*f + d*g + e*g + f*g))^2 - 64*(d*e*f*g))^2, x]
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