\[\begin{array}{l}
a)\,\,\,{99^2} + 2.99 + 1 = {\left( {99 + 1} \right)^2} = {100^2} = 10000.\\
b)\,\,{40^2} - {39^2} + {38^2} - {37^2} + ..... + {2^2} - {1^2}\\
= \left( {{{40}^2} - {{39}^2}} \right) + \left( {{{38}^2} - {{37}^2}} \right) + .... + \left( {{2^2} - {1^2}} \right)\\
= \left( {40 - 39} \right)\left( {40 + 39} \right) + \left( {38 - 37} \right)\left( {38 + 37} \right) + .... + \left( {2 - 1} \right)\left( {2 + 1} \right)\\
= 40 + 39 + 38 + 37 + .... + 2 + 1\\
= \frac{{40\left( {40 + 1} \right)}}{2} = 20.41 = 820.\\
c)\,\,\,{2019^2} - {2018^2} = \left( {2019 - 2018} \right)\left( {2019 + 2018} \right)\\
= 4037.
\end{array}\]
