a)
\(\eqalign{
& {(2{x^2} + {\rm{ }}3y)^3} = {(2{x^2})^3} + 3.{(2{x^2})^2}.3y + 3.{\rm{ }}2{x^2}.{\left( {3y} \right)^2} + {\left( {3y} \right)^3} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 8{x^6} + 3.4{x^4}.3y + 3.2{x^2}.9{y^2} + 27{y^3} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,= 8{x^6} + 36{x^4}y + 54{x^2}{y^2} + 27{y^3} \cr} \)
b)
\(\eqalign{
& {\left( {{1 \over 2}x - 3} \right)^3} = {\left( {{1 \over 2}x} \right)^3} - 3.{\left( {{1 \over 2}x} \right)^2}.3 + 3.\left( {{1 \over 2}x} \right){.3^2} - {3^3} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \;\;\;\;\;\;= {1 \over 8}{x^3} - 3.{1 \over 4}{x^2}.3 + 3.{1 \over 2}x.9 - 27 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\;\;\;\;\;\; = {1 \over 8}{x^3} - {9 \over 4}{x^2} + {{27} \over 2}x - 27 \cr} \)
