M=(100^2+98^2+....+4^2+2^2)-(101.99+99.97+...+3.1)

`M=(100^2 +98^2 +96^2 +...+4^2 +2^2 )-(101.99+99.97+97.95+...+5.3+3.1)`

`=(100^2 -101.99)+(98^2 -99.97)+(96^2 -97.95)+...+(4^2 -5.3)+(2^2 -3.1)`

`=[100^2 -(100+1)(100-1)]+[98^2 -(98+1)(98-1)]+[96^2 -(96+1)(96-1)]+...+[4^2 -(4+1)(4-1)]+[2^2 -(2+1)(2-1)]`

`=[100^2 -(100^2 -1)]+[98^2 -(98^2 -1)]+[96^2 -(96^2 -1)]+...+[4^2 -(4^2 -1)]+[2^2 -(2^2 -1)]`

`=(100^2 -100^2 +1)+(98^2 -98^2 +1)+(96^2 -96^2 +1)+...+(4^2 -4^2 +1)+(2^2 -2^2 +1)`

`=\underbrace{1+1+1...+1+1}_{50\text{ số hạng }}=1.50=50`

Vậy `M=50`

$\bullet$ Hằng đẳng thức : `a^2 -b^2 =(a-b)(a+b)`