Вправи: 328

328. Спростіть вираз.

a) (3a-1 – 3a2+ 6a+3a2- 1 : a4+ aa3+ 1) • a+a2-3 = a+1a-1;

1. 3(a+1)2a-1(a+1) • a3+ 1a(a3+ 1) = 3a+1•1a-1•a = 3(a+1)a(a-1);

2. 3a-1 – 3a+3a(a-1) = 3a-3a-3a(a-1) = -3a(a-1) = 3a(1-a);

3. 3a(1-a) • a(a+1)-3 = a+1a-1;

б) (4aa+2 – a3-8a3+8 : a3-44a2-16a+16)³ • a+216 = a3+8a-82(a3+8);

1. a3-8a3+8 • 4(a2-4a+4)a2-4 = (a3-8)•4• (a-2)2(a3+8)(a-2)(a+2) = 4(a3-8)(a-2)(a3+8)(a+2);

2. 4aa+2 – 4(a3-8)(a-2)(a3+8)(a+2) = 4a(a3+8)- (a3-8)(4a-8)(a3+8)(a+2) = 4a4+32a-4a4+ 8a3+32a-64 (a3+8)(a+2) = 8a3+64a-64(a3+8)(a+2);

3. 8a3+64a-64(a3+8)(a+2) • a+216 = a3+8a-8(a3+8)•2.