Вправи: 188

188. Спростіть вираз:

1) (a2b3- ab2 + a-bb2 – 1b) : (a+bb-a – b-aa+b + 6a2a2- b2) = –a+b2ab.

1. a2b2(b-a) + a- bb-ab2 – 1\b(b-a)b = a+a-bb-a- b(b-a)b2(b-a) = a-(a-b)2- b2+ abb2(b-a) = a2- a2+ 2ab- b2- b2+ abb2(b-a) = 3ab-2b2b2(b-a);

2. a+ b\a+bb-a – b- a\b-aa+b – 6a2b-a(b+a) = (a+b)2- (b-a)2- 6a2b-a(b+a) = a2+ 2ab+ b2- b2+ 2ab- a2- 6a2b-a(b+a) = 4ab-6a2b-a(b+a);

3. b(3a-2b)b2(b-a) : 2a(2b-3a)b-a(b+ a) = –b3a-2bb-a(b+a)b2b-a • 2a(3a-2b) = –a+b2ab.

2) (a+24a3- 4a2+ a – 2-a1-8a3 • 4a2+ 2a+12a2+ a) : (11-2a)² – 8a-12a2+ a = 1a.

1. –2-a1-8a3 • 4a2+ 2a+12a2+ a = a-28a3- 1 • 4a2+ 2a+1a(2a+1) = a-2(4a2+ 2a+1)2a-14a2+ 2a+1•a(2a+1) = a-2a2a-1(2a+1);

2. a+ 2\2a+14a3- 4a2+ a – a-2\2a-1a(4a2- 1) = 2a+1a+2- (2a-1)(a-2)a(2a-1)2(2a+1) = 2a2+ 4a+a+2-(2a2- 4a-a+2)a(2a-1)2(2a+1) = 2a2+ 5a+2-2a2+ 5a-2a(2a-1)2(2a+1) = 10aa(2a-1)2(2a+1);

3. 10aa(2a-1)2(2a+1) • (1-2a)21 = 10aa(2a+1);

4. 102a+1 – 8a-1a(2a+1) = 10a-(8a-1)a(2a+1) = 10a-8a+1a(2a+1) = 2a+1a(2a+1) = 1a.