Ответ:
1006
Объяснение:
![-x^{2020}+x^{2019}-x^{2018}+...-x^{2}+x=\\ =x^{2019}(1-x)+x^{2017}(1-x)+x(1-x)=\\=x(1-x)(x^{2018}+x^{2016}+...+x^{2}+1)](https://tex.z-dn.net/?f=-x%5E%7B2020%7D%2Bx%5E%7B2019%7D-x%5E%7B2018%7D%2B...-x%5E%7B2%7D%2Bx%3D%5C%5C%20%3Dx%5E%7B2019%7D%281-x%29%2Bx%5E%7B2017%7D%281-x%29%2Bx%281-x%29%3D%5C%5C%3Dx%281-x%29%28x%5E%7B2018%7D%2Bx%5E%7B2016%7D%2B...%2Bx%5E%7B2%7D%2B1%29)
Если n есть чётное (n = 2k)
, при k>1
![x^{n}+1 = (x + 1)(x^{n-1} - x^{n-2} +...+ x - 1)](https://tex.z-dn.net/?f=x%5E%7Bn%7D%2B1%20%3D%20%28x%20%2B%201%29%28x%5E%7Bn-1%7D%20-%20x%5E%7Bn-2%7D%20%2B...%2B%20x%20-%201%29)
или же
![x^{n} = (x + 1)(x^{n-1} - x^{n-2} +...+ x - 1)-1](https://tex.z-dn.net/?f=x%5E%7Bn%7D%20%3D%20%28x%20%2B%201%29%28x%5E%7Bn-1%7D%20-%20x%5E%7Bn-2%7D%20%2B...%2B%20x%20-%201%29-1)
для n=2 обратная ситуация
![x^{2} = (x + 1)(x-1)+1](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%3D%20%28x%20%2B%201%29%28x-1%29%2B1)
обозначим
![M_{n}=x^{n-1} - x^{n-2} +...+ x - 1](https://tex.z-dn.net/?f=M_%7Bn%7D%3Dx%5E%7Bn-1%7D%20-%20x%5E%7Bn-2%7D%20%2B...%2B%20x%20-%201)
в результате получим наш многочлен
![x(1-x)(x^{2018}+x^{2016}+...+x^{2}+1)=\\=-x(x-1)(((x+1)M_{2018}-1)+((x+1)M_{2016}-1)+...+((x+1)M_{4}-1)+((x+1)(x-1)+1)+1)=\\=-x(x-1)((x+1)M_{2018}+(x+1)M_{2016}+...+(x+1)M_{4}+(x+1)(x-1)+(-1)\frac{2018-2}{2} +1+1)=\\=x(x-1)(-(x+1)(M_{2018}+M_{2016}+...+M_{4}+(x-1))+1006)](https://tex.z-dn.net/?f=x%281-x%29%28x%5E%7B2018%7D%2Bx%5E%7B2016%7D%2B...%2Bx%5E%7B2%7D%2B1%29%3D%5C%5C%3D-x%28x-1%29%28%28%28x%2B1%29M_%7B2018%7D-1%29%2B%28%28x%2B1%29M_%7B2016%7D-1%29%2B...%2B%28%28x%2B1%29M_%7B4%7D-1%29%2B%28%28x%2B1%29%28x-1%29%2B1%29%2B1%29%3D%5C%5C%3D-x%28x-1%29%28%28x%2B1%29M_%7B2018%7D%2B%28x%2B1%29M_%7B2016%7D%2B...%2B%28x%2B1%29M_%7B4%7D%2B%28x%2B1%29%28x-1%29%2B%28-1%29%5Cfrac%7B2018-2%7D%7B2%7D%20%2B1%2B1%29%3D%5C%5C%3Dx%28x-1%29%28-%28x%2B1%29%28M_%7B2018%7D%2BM_%7B2016%7D%2B...%2BM_%7B4%7D%2B%28x-1%29%29%2B1006%29)
10^2n * 3^2 / 25^n * 2^2(n+1) = 5^2n*2^2n * 9 / 5^2n* 2^(2n+2) =9/2^2 = 9/4 = 2,25
Исходное не пишу
= 5(а-в)²(а-в-2)=5(а-в)(а-в)(а-в-2)=5(а²-2ав+в²)(а-в-2)
Вот картинка, как решила. Только перевернуть надо.