Вправи: 818

818. Скоротіть дріб:

1) 3x-6y3x = 3(x-2y)3x = x-2yx; 2) 3a+9b4a+12b = 3(a+3b)4(a+3b) = 34;

3) a2-493a+21 = (a-7)(a+7)3(a+7) = a-73; 4) 12x2-4x2-6x = -4x(3x-1)2(3x-1) = –2x;

5) x2-9x2+6x+9 = (x-3)(x+3)(x+3)2 = x-3x+3; 6) b7+b4b2+ b5 = b4(b2+1)b2(b3+1) = b²;

7) a3+643a+12 = (a+4)(a2-4a+16)3(a+4) = a2-4a+163;

8) xb-5y+5b- xyx2-25 = xb+5b-(xy+5y)x2-25 = bx+5- y(x+5)(x-5)(x+5) = bx+5- y(x+5)(x-5)(x+5) = (x+5)(b- y)(x+5)(x-5) = b- yx-5;

9) 7m2- 7m+714m3+ 14 = 7(m2- m+1)14m+1(m2- m+1) = 12(m+1) = 12m+2;

10) a2+ bc- b2+ acab+ c2- ac- b2 = a2- b2+ (ac+bc)c2- b2+ (ab+ac) = a-ba+b+ c(a+b)c-bc+b+ a(b+c) = a+b(a-b+c)b+c(a-b+c) = a+bb+c;

11) 20mn2- 20m2n+5m310mn-5m2 = 5m(4n2- 4mn+ m2)5m(2n-m) = (2n-m)22n-m = 2n – m;

12) x2- yz+xz- y2x2+ yz-xz- y2 = x2- y2+ (xz-yz)x2- y2- (xz-yz) = x-yx+y+ z(x-y)x-yx+y- z(x-y) = x-y(x+y+z)x-y(x+y-z) = x+y+zx+y-z.