Вправи: 12.8

12.8 Виконайте дії:

1) (x-2x+2 – x+2x-2) • x2-44x = –2.

1. x-2x+2 – x+2x-2 = (x-2)2-(x+2)2(x+2)(x-2) = x2-4x+4- x2-4x-4x2-4 = -8xx2-4;

2. -8xx2-4 • x2-44x = -8(x2 -4)x2 -4 • 4x = –2.

2) (a+3a-3 – a-3a+4) : 24aa2-6a+9 = a-32(a+3).

1. a+3a-3 – a-3a+3 = (a+3)2-(a-3)2(a-3)(a+3) = a2+6a+9-a2 +6a-9(a-3)(a+3) = 12a(a-3)(a+3);

2. 12a(a-3)(a+3) : 24aa2-6a+9 = 12a(a-3)2a-3a+3 • 24a = a-32(a+3).