Вправи: 279

279. Виконай ділення.

a) 16xy2- x3x2- 2xy+ y2 : x2y- 16y3x2- y2 = x(16y2- x2)(x2- y2)(x-y)2 •y • (x2- 16y2) = -x(x+y)y(x-y) = x(x+y)y(y-x);

б) x2+ 2xy+ y2y2x- 9x3 : x2- y29x2y- y3 = (x+y)2 •y • (9x2- y2)x(y2- 9x2) •(x2- y2) = -y(x+y)x(x-y) = y(x+y)x(y+x);

в) x2+ xy5x2- 5y2: x2 xyx3+ y3 = x(x+y)5(x2- y2) • x+y(x2- xy+ y2)x(x-y) = x3+ y35(x- y)2;

г) x2- 2xyx2+ 4y2 : (x-2y)2x4- 16y4 = xx-2y• (x2- 4y2)(x2+ 4y2)(x2+ 4y2) •(x- 2y)2 = x(x2- 4y2)x-2y = x(x + 2y).