Question

the square root of (2x+y)^2-4(x+2y) (x-y)

Answer 1

expand the terms
4x² + y² + 4xy - 4 (x²  - xy + 2yx -2y²)
=  9 y² 
square root is  3 y  or  - 3 y

Answer 2

$(2x+y)^2-4(x+2y)(x-y)=(*)\\-----------------------------\\(2x+y)^2=(2x)^2+2(2x)(y)+y^2=4x^2+4xy+y^2\\\\used:(a+b)^2=a^2+2ab+b^2\\----------------\\-4(x+2y)=-4x-8y\\\\(-4x-8y)(x-y)=-4x^2+4xy-8xy+8y^2=-4x^2-4xy+8y^2\\------------------------------\\(*)=4x^2+4xy+y^2-4x^2-4xy+8y^2=9y^2\\====================================$

$\sqrt{9y^2}=\sqrt9\times\sqrt{y^2}=3|y|\\\\If\ y\geq0\ then\ 3|y|=3y\\\\if\ y < 0\ the\ 3|y|=-3y$