Вправи: 178

178. Виконайте дії:

1) a+2a2- 2a+1 : a2- 43a-3 – 3a-2 = a+2 • 3 • (a-1)(a-1)2(a-2)(a+2) – 3a-2 = 3a-1(a-2) – 3\a-1a-2 = 3-3(a-1)a-1(a-2) = 3-3a+3a-1(a-2) = 6-3aa-1(a-2) = -3(a-2)a-1(a-2) = –3a-1 = 31-a;

2) b2+ 3bb3+ 9b • (b-3b+3 + b+3b-3) = b(b+3)b(b2+ 9) • (b-3)2+ (b+3)2b-3(b+3) = b+3•(b2- 6b+9+ b2+ 6b+9)bb2+ 9b-3(b+3) = b+3(2b2+ 18)bb2+ 9b-3(b+3) = 2(b2+ 9)b2+ 9(b-3) = 2b-3;

3) (3c+ 1\3c+13c -1 – 3c- 1\3c-13c+1) : 2c6c+2 = (3c+1)1- (3c-1)23c-1(3c+1) • 2(3c+1)2c = 9c2+ 6c+1-(9c2- 6c+1)3c-1(3c+1) • 3c+1c = 9c2+ 6c+1-9c2+ 6c-13c-1(3c+1) • 3c+1c = 12c(3c+1)3c-13c+1 • c = 123c-1;

4) (1a2- 4ab+4b2 – 14b2- a2) : 2aa2- 4b2 = (1\a+2b(a-2b)2 + 1\a-2ba-2b(a+2b)) • a-2b(a+2b)2a = a+2b+a-2b(a-2b)2(a+2b) • a-b(a+2b)2a = 2aa-2b(a+2b)(a-2b)2a+2b • 2a = 1a-2b;

5) (a-8a2- 10a+25 – aa2- 25) : a-20(a-5)2 = (a- 8\a+5(a-5)2 – a\a-5a-5(a+5)) : a-20(a-5)2 = a+5a-8- a(a-5)(a-5)2(a+5) • (a-5)2a-20 = a2- 8a+5a-40- a2+ 5a(a-5)2(a- 5)2(a+5)(a-20) = 2a-40a+5(a-20) = 2(a-20)a+5(a-20) = 2a+5;

6) (2x+1x2+ 6x+9 – x-2x2+ 3x) : x2+ 6x3- 9x = (2x+ 1\x(x+3)2 – x- 2\x+3x(x+3):x2+ 6x3- 9x = x2x+1- (x+3)(x-2)x(x+3)2 • xx-3(x+3)x2+ 6 = 2x2+ x-(x2- 2x+3x-6)x(x+3)2 • xx-3(x+3)x2+ 6 = 2x2+ x- x2- x+6 • xx-3(x+3)x(x+3)2(x2+ 6) = x2+ 6(x-3)x+3(x2+ 6) = x-3x+3.