Ta có:
$x=9 ⇒ x+1 = 10$
Thay $x+1=10$ vào $A$ ta có :
$A = x^{100} - (x+1).x^{99}+ (x+1).x^{98} - (x+1).x^{97} + ..... + (x+1).x^2 - (x+1)x+1$
$A = x^{100} - x^{100} - x^{99} + x^{99} + x^{98} - x^{98} - x^{97} + ..... + x^3 + x^2 - x^2 - x +1$
$A = -x + 1$
$A = -9 + 1$
$A = -8$