(1,2x+1,1y)^6 = (1+2x+1y)^6 = 1^6 + 6(1^5)(2x+1y) + 15(1^4)(2x+1y)^2 + 20(1^3)(2x+1y)^3 + 15(1^2)(2x+1y)^4 + 6(1)(2x+1y)^5 + (2x+1y)^6= 1 + 6(2x + 1y) + 15(4x^2 + 4xy + y^2) + 20(8x^3 + 12x^2y + 6xy^2 + y^3) + 15(16x^4 + 32x^3y + 24x^2y^2 + 8xy^3 + y^4) + 6*(32x^5 + 80x^4y + 80x^3y^2 + 40x^2y^3 + 10xy^4 + y^5) + (64x^6 + 192x^5y + 240x^4y^2 + 160x^3y^3 + 60x^2y^4 + 12xy^5 + y^6)= 1 + 12x + 6y + 60x^2 + 60xy + 15y^2 + 120x^3 + 180x^2y + 90xy^2 + 20y^3 + 240x^4 + 480x^3y + 360x^2y^2 + 120xy^3 + 15y^4 + 192x^5 + 480x^4y + 480x^3y^2 + 240x^2y^3 + 60xy^4 + 6y^5 + 64x^6 + 192x^5y + 240x^4y^2 + 160x^3y^3 + 60x^2y^4 + 12xy^5 + y^6= 64x^6 + 192x^5y + 240x^4y^2 + 10x^3 + 480x^3y + 360x^2y^2 + 120y^2 + 240x^4 + 480x^3y + 360x^2y^2 + 120xy^3 + 15y^4 + 192x^5 + 480x^4y + 480x^3y^2 + 240x^2y^3 + 60xy^4 + 6y^5 + 64x^6 + 192x^5y + 240x^4y^2 + 160x^3y^3 + 60x^2y^4 + 12xy^5 + y^6
(1,2x+1,1y)^6 = (1+2x+1y)^6 = 1^6 + 6(1^5)(2x+1y) + 15(1^4)(2x+1y)^2 + 20(1^3)(2x+1y)^3 + 15(1^2)(2x+1y)^4 + 6(1)(2x+1y)^5 + (2x+1y)^6
= 1 + 6(2x + 1y) + 15(4x^2 + 4xy + y^2) + 20(8x^3 + 12x^2y + 6xy^2 + y^3) + 15(16x^4 + 32x^3y + 24x^2y^2 + 8xy^3 + y^4) + 6*(32x^5 + 80x^4y + 80x^3y^2 + 40x^2y^3 + 10xy^4 + y^5) + (64x^6 + 192x^5y + 240x^4y^2 + 160x^3y^3 + 60x^2y^4 + 12xy^5 + y^6)
= 1 + 12x + 6y + 60x^2 + 60xy + 15y^2 + 120x^3 + 180x^2y + 90xy^2 + 20y^3 + 240x^4 + 480x^3y + 360x^2y^2 + 120xy^3 + 15y^4 + 192x^5 + 480x^4y + 480x^3y^2 + 240x^2y^3 + 60xy^4 + 6y^5 + 64x^6 + 192x^5y + 240x^4y^2 + 160x^3y^3 + 60x^2y^4 + 12xy^5 + y^6
= 64x^6 + 192x^5y + 240x^4y^2 + 10x^3 + 480x^3y + 360x^2y^2 + 120y^2 + 240x^4 + 480x^3y + 360x^2y^2 + 120xy^3 + 15y^4 + 192x^5 + 480x^4y + 480x^3y^2 + 240x^2y^3 + 60xy^4 + 6y^5 + 64x^6 + 192x^5y + 240x^4y^2 + 160x^3y^3 + 60x^2y^4 + 12xy^5 + y^6