Вправи: 468

468. Спростіть вираз:

(4x2- 6x – 26- x + 1) • (2x2- 4 – 2x3- 6x2+12x-8) = 1x2- 4.

1. 4x3- 6x – 26- x + 1 = 4x(x-6) + 2x-6 + 1 = 4+2x+ x2-6xx(x-6) = x2- 4x+4x(x-6);

2. x³ – 6x² + 12x – 8 = (x – 2)(x² + 2x + 4) – 6x(x – 2) = (x – 2)(x² + 2x + 4 – 6x) = (x – 2)(x² – 4x + 4) = (x – 2)(x – 2)² = (x – 2)³;

3. 1x2- 4 – 2(x-2)3 = 1(x-2)(x+2) – 2(x-2)3 = (x-2)2-2(x+2)(x-2)3(x+2) = x2- 4x+4-2x-4(x-2)3(x+2) = x2- 6x(x-2)3(x+2);

4. x2- 4x+4x(x-6) • x2- 6x(x-2)3(x+2) = (x-2)2• x(x-6)x(x-6)(x-2)3(x+2) = 1(x-2)(x+2) = 1x2- 4.