Question

Is `4x^2 + 8xy + 4y^2` a perfect square?

Answer 1

Yes, as long as `2x+2y` is an integer.

`4x^2+8xy+4y^2=(2x+2y)^2`

Explanation:

`4x^2+8xy+4y^2 = 4x^2+4xy+4xy+4y^2`

`=[4x^2+4xy]+[4xy+4y^2]`

`=2x(2x+2y)+2y(2x+2y)`

`=(2x+2y)(2x+2y)`

`=(2x+2y)^2`