1, 99² + 99.2 + 1
= (99+1)²
=100²
=10000
2, ( 10² + 8² + 6² + 4² + 2²) - (9² + 7² + 5² + 3² + 1²)
= 10² + 8² + 6² + 4² + 2² - 9² - 7² - 5² - 3² - 1²
= (10² - 9²) + (8² - 7²) + (6² - 5²) + (4²- 3²) + (2²-1²)
=(10-9)(10+9) + (8-7)(8+7) + (6-5)(6+5) + (4-3)(4+3) + (2-1)(2+1)
=10+9+8+7+6+5+4+3+2+1
=(10+1).10/2
=55
3, 2020²- 2019(2020+1)
=2020² - 2019.2020 - 2019
= 2020(2020-2019)-2019
=2020 - 2019
=1
4, 3(2²+1)(2^4+1)...(2^2018+1)(2^2020+1)
=(2²-1)(2²+1)(2^4+1)...(2^2018+1)(2^2020+1)
=(2^4-1)(2^4+1)...(2^2018+1)(2^2020+1)
....
=2^4040-1
