Question

-4 x^2 + 4 x y - y^2 factorize

Answer 1

let F = -4 (x² - x y + 1/4 y²)   Make F = 0 and find roots of the equation. If they are α and β then  -4 (x -α)(x - β) will be the answer.
for x² - xy + 1/4 y² =0    =>  α & β are =  (1 +- √1 - 4*1/4)/2 = 1/2     
both roots are same
so F = -4 (x - 1/2)²

Answer 2

$Use:(a-b)^2=a^2-2ab+b^2\\\\\\-4x^2+4xy-y^2=-[(2x)^2-2\cdot2x\cdot y+y^2]=-(2x-y)^2\\\\=-(2x-y)(2x-y)$