Вправи: 170 (1-2)

170. Спростіть вираз:

1) x2+ 14x+49x+6 : (13x+6 – x + 6) = 7+x7-x.

1. 13x+6 – (x – 6) = 13x+6 – x- 6\x+61 = 13-x-6(x+6)x+6 = 13-(x2- 36)x+6 = 13- x2+ 36x+6 = 49- x2x+6;

2. (x+7)2x+6 • x+67-x(7+x) = 7+x7-x;

2) (c – 2c-9c+8) : c2+ 3cc2- 64 + 24c = c – 5.

1. c\c+81 – 2c-9c+8 = cc+8- (2c-9)c+8 = c2+ 8c-2c+9c+8 = c2+ 6c+9c+8;

2. (c+3)2c+8 • c-8(c+8)c(c+3) = c+3(c-8)c = c2- 5c-24c;

3. c2- 5c-24c + 24c = c2- 5c-24+24c = c2- 5cc = c(c-5)c = c – 5;

3) (36x2- 9 – x-3x+3 – 3+x3-x) : 63-x = –2.

1. 36x-3(x+3) – x- 3\x-3x+3 – 3+ x\x+33-x = 36-(x-3)2+ (x+3)2x-3(x+3) = 36-x2- 6x+9+ (x2+ 6x+9)x-3(x+3) = 36- x2+ 6x-9+ x2+ 6x+9x+3(x+3) = 12x+36x-3(x+3) = 12(x+3)x-3(x+3) = 12x-3;

2. 12x-3 • 3-x6 = 12(x-3)x-3 • 6 = –2;

4) (2y-1y2+ 2y+4 + 9y+6y3- 8 + 1y-2) • y2- 418 = y+26.

1. 2y- 1\y-2y2+ 2y+4 + 9y+6y-2(y2+ 2y+4) + 1\y2+2y+4y-2 = y-22y-1+ 9y+6+(y2+ 2y+4)y-2(y2+ 2y+4) = 2y2- y-4y+2+9y+6+ y2+ 2y+4y-2(y2+ 2y+4) = 3y2+ 6y+12y-2(y2+ 2y+4) = 3y2+ 6y+12y-2(y2+ 2y+4) = 3(y2+ 2y+4)y-2(y2+ 2y+4) = 3y-2;

2. 3y-2 • y-2(y+2)18 = y+26.