\(\eqalign{
& a)\,\,{\left( {2 + xy} \right)^2} = {2^2} + 2.2.xy + {\left( {xy} \right)^2} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\; = 4 + 4xy + {x^2}{y^{2}} \cr} \)
\(\eqalign{
& b)\,\,{\left( {5 - 3x} \right)^2} = {5^2} - 2.5.3x + {\left( {3x} \right)^2} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\; = 25 - 30x + 9{x^2} \cr} \)
\(\eqalign{
& c)\,\,(5 - {x^2})(5 + {x^2}) = {5^2} - {({x^2})^2} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\;\;\; = 25 - {x^4} \cr} \)
\(\eqalign{
& d)\,\,{\left( {5x - 1} \right)^3} = {\left( {5x} \right)^3} - 3.{\left( {5x} \right)^2}.1 + 3.5x{.1^2} - {1^3} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \;= 125{x^3} - 75{x^2} + 15x - 1 \cr} \)
\(\eqalign{
& e)\left( {2x - y} \right)(4{x^2} + 2xy + {y^2}) \cr
& = \left( {2x - y} \right)\left[ {{{\left( {2x} \right)}^2} + 2x.y + {y^2}} \right] \cr
& = {\left( {2x} \right)^3} - {y^3} = 8{x^3} - {y^3} \cr} \)
\(\eqalign{
& f)\,\,\,\left( {x + 3} \right)({x^2} - 3x + 9) \cr
& = \left( {x + 3} \right)({x^2} - x.3 + {3^2}) \cr
& = {x^3} + {3^3} = {x^3} + 27 \cr} \)
