Вправи: 842

842. Спростіть вираз:

1) (a+4a-4 – a-4a+4) • 16- a232a3 = (a+4)2- (a-4)2a-4(a+4) • -a-4(a+4)32a3 = a+4+a-4(a+4-a+4)32a3 = 2a • 832a3 = 12a2;

2) (7x – 4xx-3) : 14x-503x-9 = 7xx-3- 4xx-3 • 3(x-3)2(7x-25) = 7x2- 21x-4x•4(x-3)x-3 • 2(7x-25) = 7x2- 25x • 27x-25 = 2x(7x-25)7x-25 = 2x;

3) 2aa-2 + a+78-4a • 327a+ a2 = 2aa-2 + a+7 • 3242-a • a(a+7) = 2aa-2 + 8a(2-a) = 2a\aa-2 – 8a(a-2) = 2a2- 8a(a-2) = 2a-2(a+2)a(a-2) = 2a+4a;

4) (9cc-8 + 7cc2- 16c+64) : 9c-65c2- 64 – 8c+64c-8 = (9c\c-8c-8 + 7c(c-8)2) • c-8(c+8)9c-65 = 9c2- 72c+7c(c-8)2 • c-8(c+8)9c-65 – 8c+64c-8 = c9c-65(c+8)(c-8)2(9c-65) – 8c+64c-8 = c(c+8)c-8 – 8c+64c-8 = c2+ 8c-8c-64c-8 = c-8(c+8)(c-8) = c + 8;

5) (a2a+b – a3a2+ ab+ b2) : (aa-b – a2a2- b2) = a2a2+ ab+ b2- a3(a+b)a+b(a2+ ab+ b2) : aa+b- a2a-b(a+b) = a4+ a3b+ a2b2- a4- a3ba+b(a2+ ab+ b2) • a-b(a+b)a2+ ab+ b2 = a2b2a-b(a+b)a+ba2+ ab+ b2•ab = ab(a-b)a2+ ab+ b2 = a2b-ab2a2+ ab+ b2;

6) (bb+6 + 36+ b236- b2 – bb-6) : 6b+ b2(6-b)2 = (bb+6 – 36+ b2b-6(b+6) – bb-6) : 6b+b2 (6-b)2 = b6-b+ 36+ b2- b(b+6)b-6(b+6) • (b-6)2b(b+6) = b2- 6b- b2- 36- b2- 6bb-6(b+6) • (b-6)2b(b+6) = b2+ 12b+3b•(b-6)2b-3b+6•(b+6) = –b-6b = 6-bb;

7) (2xx3+ 1 : 1-xx2- x+1 + 2x-1) • x2- 2x+1 4 : x-1x+1 = (2x • (x2- x+1)x+1x2- x+1(1-x) + 2x-1) • (x-1)2 • (x+1)4 • (x-1) = (-2xx+1(x-1) + x\x+1x-1) • x-1(x+14 = -2x+2x+1x-1(x+1) • x-1(x+1)4 = 14.