Question

Разложить на множители выражение: 4(x-y)^2 - (x+y)^2

Answer 1

Ответ:

(2(x-y)-(x+y))*(2(x-y)+(x+y))

(2x-2y-(x+y))*(2(x-y)+(x+y))

(2x-2y-x-y)*(2x-2y+x+y)

(x-3y)*(3x-y)

Answer 2

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