Вправи: 221

221. Спростіть вираз:

1) (8x2+ 2x8x3- 1 – 2x+14x2+ 2x+1) • (1 + 2x+12x – 4x2+ 10x4x2+ 2x) = 8x2+ 2x-(4x2- 1)2x-1(4x2+ 2x+1) • 4x2+ 2x+(2x+1)2- 4x2- 10x2x(2x+1) = 4x2+ 2x+12x-1(4x2+ 2x+1) • 4x2+ 2x+4x2+ 4x+1-4x2- 10x2x(2x+1) = 12x-1 • 4x2- 4x+12x(2x+1) = (2x-1)22x-1 • 2x(2x+1) = 2x-12x(2x+1).

2) p2- 2p+14 • (2pp3+ 1 : 1-pp2- p+1 + 2p-1) : p-1p+1.

1. 2pp3+ 1 : 1-pp2- p+1 = 2p(p2- p+1)p+1p2- p+1(1-p) = 2pp+1(1-p);

2. 2pp+1(1-p) + 2p-1 = 2pp+1(1-p) –21-p = 2p-2(p+1)p+1(1-p) = -2p+11-p;

3. p2- 2p+14 • -2p+1(1-p) : p-1p+1 = (p-1)2 • -2 • (p+1)-4 • p+1p-1 • (p-1) = 12.