Вправи: 205

205. Спростіть вираз:

1) 16x+2 : (x+2x-2 – 16x2- 4 – x-2x+2) = 2.

1. x+2x-2 – 16x2- 4 – x-2x+2 = (x+2)2-16-(x-2)2(x-2)(x+2) = x2+ 4x+4-16-x2 +4x-4(x-2)(x+2) = 8x-16x-2(x+2) = 8(x-2)(x-2)(x+2) = 8x+2;

2. 16x+2 : 8x+2 = 16(x+2)x+2 • 8 = 2.

2) (5a+1a-2 + 5a-1a+2) • a2- 45a2+2 = 2.

1. 5a+1a-2 + 5a-1a+2 = 5a+1a+2+5a-1(a-2)(a-2)(a+2) = 5a2+10a+ a+2+5a2-10a- a+2(a-2)(a+2) = 10a2+4a2- 4;

2. 10a2+4a2- 4 • a2- 45a2+2 = 2(5a2+2)(a2 -4)(a2 -4)(5a2+2) = 2.