(2+1)^6 = C(6,0) 2^6 + C(6,1) 2^5 1 + C(6,2) 2^4 1^2 + C(6,3) 2^3 1^3 + C(6,4) 2^2 1^4 + C(6,5) 2^1 1^5 + C(6,6) 2^0 1^= 1 64 + 6 32 + 15 16 + 20 8 + 15 4 + 6 2 + 1 = 729
(x+y)^7 = C(7,0) x^7 + C(7,1) x^6 y + C(7,2) x^5 y^2 + C(7,3) x^4 y^3 + C(7,4) x^3 y^4 + C(7,5) x^2 y^5 + C(7,6) x y^6 + C(7,7) y^7
(x-y)^5 = C(5,0) x^5 - C(5,1) x^4 y + C(5,2) x^3 y^2 - C(5,3) x^2 y^3 + C(5,4) x y^4 - C(5,5) y^5
(2x-1)^6 = C(6,0) (2x)^6 - C(6,1) (2x)^5 1 + C(6,2) (2x)^4 1^2 - C(6,3) (2x)^3 1^3 + C(6,4) (2x)^2 1^4 - C(6,5) (2x) 1^5 + C(6,6) 1^= 64x^6 - 192x^5 + 240x^4 - 160x^3 + 60x^2 - 12x + 1
(2+1)^6 = C(6,0) 2^6 + C(6,1) 2^5 1 + C(6,2) 2^4 1^2 + C(6,3) 2^3 1^3 + C(6,4) 2^2 1^4 + C(6,5) 2^1 1^5 + C(6,6) 2^0 1^
= 1 64 + 6 32 + 15 16 + 20 8 + 15 4 + 6 2 + 1
= 729
(x+y)^7 = C(7,0) x^7 + C(7,1) x^6 y + C(7,2) x^5 y^2 + C(7,3) x^4 y^3 + C(7,4) x^3 y^4 + C(7,5) x^2 y^5 + C(7,6) x y^6 + C(7,7) y^7
(x-y)^5 = C(5,0) x^5 - C(5,1) x^4 y + C(5,2) x^3 y^2 - C(5,3) x^2 y^3 + C(5,4) x y^4 - C(5,5) y^5
(2x-1)^6 = C(6,0) (2x)^6 - C(6,1) (2x)^5 1 + C(6,2) (2x)^4 1^2 - C(6,3) (2x)^3 1^3 + C(6,4) (2x)^2 1^4 - C(6,5) (2x) 1^5 + C(6,6) 1^
= 64x^6 - 192x^5 + 240x^4 - 160x^3 + 60x^2 - 12x + 1