Tính nhanh giá trị các biểu thức sau:

a) \({202^2} = {\left( {200 + 2} \right)^2} = {200^2} + 2.200.2 + {2^2} = 40\,\,000 + 800 + 4 = 40\,\,804\).

b) \(299\,.\,301 = \left( {300 - 1} \right).\left( {300 + 1} \right) = {300^2} - 1 = 90\,\,000 - 1 = 89\,\,999\).

c) \({95^3} + {15.95^2} + 3.95.25 + {5^3}\)

\( = {95^3} + {3.95^2}.5 + {3.95.5^2} + {5^3}\)

\( = {\left( {95 + 5} \right)^3} = {100^3} = 1\,\,000\,\,000\).

d) \(9\left( {{{10}^2} + 10 + 1} \right) + 100\left( {{{98}^2} + 392 + {2^2}} \right)\)

\( = \left( {10 - 1} \right)\left( {{{10}^2} + 10 + 1} \right) + 100\left( {{{98}^2} + 2.98.2 + {2^2}} \right)\)

\( = {10^3} - 1 + 100{\left( {98 + 2} \right)^2}\)

\( = 1\,000 - 1 + {100.100^2}\)

\( = 999 + 100.10\,\,000\)

\( = 999 + 1\,\,000\,\,000\)

\[ = 1\,\,000\,\,999\].