Product simply means multiply:
(2x+7y)^2 -> (2x+7y)(2x+7y)(2x+7y)2→(2x+7y)(2x+7y)
Using FOIL or an alternative method:
(color(red)(2x)color(blue)(+7y))(color(red)(2x)color(blue)(+7y))(2x+7y)(2x+7y)
color(red)(2x) xx color(red)(2x=4x^22x×2x=4x2
color(red)(2x) xx color(blue)(7y)=color(green)(14xy)2x×7y=14xy
color(blue)(7y) xx color(red)(2x)=color(green)(14xy)7y×2x=14xy
color(blue)(7y) xx color(blue)(7y)=color(blue)(49y^2)7y×7y=49y2
Collecting like terms:
color(red)(4x^2)+color(blue)(49y^2)+color(green)(14xy)+color(green)(14xy) -> color(red)(4x^2)+color(blue)(49y^2)+color(green)(28xy)4x2+49y2+14xy+14xy→4x2+49y2+28xy
This is the final answer.
Remember you can always factorise this to check.