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.

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