$1,2x+1,1y$^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$8x^3+12x^{2}y+6x{y}^2+y^3$ + 15$16x^4+32x^{3}y+24x^2{y}^2+8x{y}^3+y^4$ + 6*$32x^5+80x^{4}y+80x^3{y}^2+40x^2{y}^3+10x{y}^4+y^5$ + $64x^6+192x^{5}y+240x^4{y}^2+160x^3{y}^3+60x^2{y}^4+12x{y}^5+y^6$ = 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