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

1 Answer
Apr 15, 2018

4x^2+49y^2+28xy4x2+49y2+28xy

Explanation:

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+14xy4x2+49y2+28xy

This is the final answer.

Remember you can always factorise this to check.