How do you find the product #(2x+7y)^2#?

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Answer 1 · 2018-04-15T11:56:09

#4x^2+49y^2+28xy#

Product simply means multiply:

#(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))#

#color(red)(2x) xx color(red)(2x=4x^2#

#color(red)(2x) xx color(blue)(7y)=color(green)(14xy)#

#color(blue)(7y) xx color(red)(2x)=color(green)(14xy)#

#color(blue)(7y) xx color(blue)(7y)=color(blue)(49y^2)#

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)#

This is the final answer.

Remember you can always factorise this to check.