Вправи: 202

202. Спростіть вираз:

1) 9cx316ab • 2ab2cxy • 4by23ax2 = 9cx3 • 2ab2 • 4by216ab •cxy • 3ax2 = 6b2x3y24ax3y = 3b2y2a;

2) x2y2- 4y24xy • x2y2xy- x2y = (x2y2- 4y2) • x2y4xy(2xy- x2y) = y2x2- 4• x2y4xy •xy(2-x) = x2y3x-2(x+2)4x2y2(2-x) = –yx-2(x+2)4(x-2) = –y(x+2)4;

3) a2- b2a2+ b2 • a4- b4a2- 2ab+ b2 = (a2- b2)(a4- b4)(a2+ b2)(a2- 2ab+ b2) = a-ba+ba2- b2(a2+ b2)(a2+ b2) •(a-b)2 = a+ba-b(a+b)a-b = (a + b)².

4) x2+ xyx2- y2 • x3- y3xy(x+y) = (x2+ xy)(x3- y3)(x2- y2) •xy(x+y) = xx+yx-y(x2+ xy+ y2)x-yx+y•xy •(x+y) = x2+ xy+ y2y(x+y);

5) x2- 2xy+ y2x2- xy+ y2 • x3+ y3x-y = (x2- 2xy+ y2)(x3+ y3)(x2- xy+ y2) •(x-y) = (x-y)2 •x+y•(x2- xy+ y2)(x2- xy+ y2) •(x-y) = x-y(x+y)1 = x² – y²;

6) x2+ y2- xya2- b2 • a2+ b2- 2abx3+ y3 = (x2+ y2- xy) • (a2+ b2- 2ab)(a2- b2) •(x3+ y3) = (x2- xy+ y2) • (a-b)2a-b•a+b•x+y(x2- xy+ y2) = a-ba+b(x+y).