Question

Розкладіть на множники вираз: (х-у)²-z²-4х²+4ху+4xz

Answer 1

a^2-b^2=(a-b)(a+b)
(x-y)^2-z^2=(x-y-z)(x-y+z)
-4x^2+4xy+4xz=-4x(x-y-z)
(x-y-z)(x-y+z-4x)=(x-y-z)(z-y-3x)

Answer 2

$(x-y)^2-(z-2x)^2+4xy=x^2-2xy+y^2+4xy-(z-2x)^2=\ =(x+y)^2-(z-2x)^2=(x+y-z+2x)(x+y+z-2x)=\ =(3x+y-z)(y+z-x)$