Sửa đề: x=21

=>x-1=20

\(A=x^{10}+x^9\left(x-1\right)+x^8\left(x-1\right)+...+x^3\left(x-1\right)+x^2\left(x-1\right)+x\left(x-1\right)\)

\(=x^{10}+x^{10}-x^9+x^9-x^8+...+x^3-x^2+x^2-x\)

\(=2x^{10}-x=2\cdot21^{10}-21\)

\(F=x^{10}+20x^9+20x^8+...20x^2+20x=x^9\left(x+19\right)+x^8\left(x+19\right)+...+x^2\left(x+19\right)+x\left(x+19\right)+x=x^9\left(-19+19\right)+x^8\left(-19+19\right)+...+x^2\left(-19+19\right)+x\left(-19+19\right)-19=x^9.0+x^8.0+...+x.0-19=-19\)

a) Có x = 2020 => x + 1 = 2021. Thay 2021 = x + 1 vào A

\(A=x^6-\left(x+1\right)^5+\left(x+1\right)x^4-\left(x+1\right)x^3+\left(x+1\right)x^2-\left(x+1\right)x+x+1\)

\(A=x^6-x^6-x^5+x^5+x^4-x^4-x^3+x^3+x^2-x^2-x+x+1\)

\(A=1\)

b) Có x = -19 => x - 1 = -20 => - ( x - 1 ) = 20. Thay 20 = - ( x - 1) vào B

\(B=x^{10}-\left(x-1\right)x^9-\left(x-1\right)x^8-\left(x-1\right)x^7-...-\left(x-1\right)x^2-\left(x-1\right)x-x+1\)

\(B=x^{10}-x^{10}+x^9-x^9+...+x^2-x^2+x-x+1\)

\(B=1\)

Chúc bạn học tốt!!!