Вправи: 1104

1104. Спростіть вираз:

1) (x2+ xx2- y2- x2- xx2- y2)22x3y : (xy + yx – 2) = (x+ y)2x-y.

1) (x2+ xx2- y2 – x2- xx2- y2)² = x² + xx2-y2 – 2x2+ xx2- y2)(x2- xx2- y2) + x² – xx2- y2 = 2x² – 2x4- x4+ x2y2 = 2x² – 2x2y2 = 2x² – 2|x||y| = 2x² – 2xy.

2. xy + yx – 2 = xy + yx – 2 = x-2xy+ yxy = (x- y)2xy.

3. 2x2- 2xy2x3y : (x- y)2xy = 2xx-y • xy2xxy(x- y)2 = x-y(x- y)2 = x- y(x+ y)(x- y)2 = x+ yx- y = (x+ y)2x-y.

2) (b-ab+a+ b-a + b-ab2- a2+ a+b) : b2a2- 1 = 1.

1. b-ab2- a2+ a-b = b-ab-ab+a- (b-a)2 = (b-a)2b-a(b+a- b-a) = b-ab+a- b-a.

2. b-ab+a+ b-a + b-ab+a- b-a= b-a • b+a- b-a+ b+a+ b-ab+a+ b-a(b+a- b-a) = b-a • 2b+ab+a-(b-a) = 2b2- a22a = b2- a2a.

3. b2- a2a : b2- a2a2 = b2- a2a : b2- a2|a| = 1.