a)
\(\eqalign{
& {101^2} = {\left( {100 + 1} \right)^2} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = {100^2} + 2.100.1 + {1^2} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = 10000 + 200 + 1 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = 10201 \cr} \)
b)
\(\eqalign{
& {199^2} = {\left( {200 - 1} \right)^2} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = {200^2} - 2.200.1 + {1^2} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = 40000 - 400 + 1 = 39601 \cr} \)
c)
\(\eqalign{
& 47.53 = \left( {50 - 3} \right)\left( {50 + 3} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {50^2}-{3^2} = 2500 - 9 = 2491 \cr} \)
