Đáp án:
$A = 0$
Giải thích các bước giải:
Ta có : $x = 2021$
⇔ $x - 2 = 2019$
Lại có :
$A = x^{2021} - 2019x^{2020} - 2.2019x^{2019} - 2^{2}.2019x^{2018} -...- 2^{2019}.2019x - 2^{2020}.2021$
$⇔ A = x^{2021} - ( x - 2 )x^{2020} - 2.( x - 2 )x^{2019} - 2^{2}.( x - 2 )x^{2018} -...- 2^{2019}.( x - 2 )x - 2^{2020}x$
$⇔ A = x^{2021} - x^{2021} + 2x^{2020} - 2x^{2020} + 2^{2}.x^{2019} - 2^{2}.x^{2019} + 2^{3}.x^{2018} -...- 2^{2019}x^{2} + 2^{2020}x - 2^{2020}x$
$⇔ A = 0 + 0 + 0 + 0 +...+ 0 + 0$
$⇔ A = 0$
