(a+1)(a-1)(a^2+1)(a^4+1)(a^8+1)
=(a^2-1))(a^2+1)(a^4+1)(a^8+1)
=(a^4-1)(a^4+1)(a^8+1)
=(a^8-1)(a^8+1)
=a^16-1
100^2-99^2+98^2-97^2+…+2^2-1^2
=100^2-(100-1)^2+98^2-(98-1)^2+…+2^2-(2-1)^2
=200-1+196-1+…+4-1
=5100-50
=5050