Question

разложите на множители


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

Answer 1

$x^2-4x-y^2+4y=left(x^2-y^2right)+left(-4x+4yright)=\\=left(x^2-y^2right)-4left(x-yright)=(x-y)(x+y)-4(x-y)=\\=left(x-yright)left(left(x+yright)-4right)=(x-y)(x+y-4).$