Вправи: 228

228. Спростіть вираз:

1) 4x-y2x2+ 2xy : xy-4x28x2- 8y2 = 4x-y2x2+ 2xy • 8x2- 8y2xy-4x2 = 4x-y(8x2- 8y2)(2x2+ 2xy)(xy-4x2) = 4x-y•8(x2- y2)2x •x+y•x(y-4x) = 4x-y•8 •x-y(x+y)2x •x+y•x(4x-y) = –4(x-y)x2 = 4(y-x)x2;

2) 10b2- 10ab9a2+ 9ad : 5ab3d2+ 3ad = 10b2- 10ab9a2+ 9ad • 3d2+ 3ad5ab = (10b2- 10ab) • (3d2+ 3ad)(-a2+ 9ad) •5ab = 10bb-a•3d(d+a)9aa+d•5ab = 2d(b-a)3a2;

3) 9(c-d)2cd2+ d3 : 3d2- 3c2d4 = 9(c-d)2cd2+ d3 • d43d2- 3c2 = 9(c-d)2 • d4(cd2+d3)(3d2- 3c2) = 9(c-d)2• d4d2c+d•3(d2- c2) = 3c-d2• d2c+dd-cd+c = 3d-c2 • d2c+d•d+c = 3d2d-cc+d2;

4) 89(x-2x-1)² : (4-2x)3(3-3x)2 = 89 • (x-2)2(x-1)2 • (3-3x)2(4-2x)3 = 8 • (x-2)2•(3-3x)29 •(x-1)2 •(4-2x)3 = 8(x-2)2 • (3 •1-x)29(x-1)2 •(2 •(2-x))3 = 8(x-2)2 •9 • (1-x)29(x-1)2 •8 • (2-x)3 = (2-x)2 • (x-1)2(x-1)2 • (2-x)3 = 12-x.