Вправи: 521

521. Скоротіть дріб:

1) a2- 7a+ 7 = a2- (7)2a+ 7 = a- 7(a+ 7)a+ 7 = a – 7;

2) 3- b3- b2 = 3- b(3)2- b2 = (3- b)3- b(3+ b) = 13+ b;

3) c-9c- 3 = (c)2- 32c- 3 = c- 3(c+ 3)c- 3 = c + 3;

4) a-ba+ b = (a)2- (b)2a+ b = a- b(a+ b)(a+ b) = a – b;

5) 5a- 7b25a-49b = 5a- 7b(5a)2- (7b)2 = (5a- 7b)5a- 7b(5a+ 7b) = 15a+ 7b;

6) 100a2- 9b10a+3b = (10a)2- (3b)210a+3b = 10a-3b(10a+3b)(10a+3b) = 10a – 3b;

7) 2 - 16 - 3 = 2 - 13 • 2 - 3 = (2 - 1)3(2- 1) = 13 = 3(3)2 = 33;

8) 35 + 107 + 2 = 7 • 5 + 5 • 27 + 2 = 57+ 27+ 2 = 5;

9) 15 - 65 - 10 = 5 • 3 - 3 • 2(5)2 - 5 • 2 = 3(5 - 2)5(5 - 2) = 35 = 3 • 5(5)2 = 155;

10) 13 - 1313 = (13)2 - 1313 = 13(13- 1)13 = 13 – 1;

11) a+2ab+ ba+ b = (a)2 + 2ab + (b)2a + b = (a + b)2(a + b) = a + b;

12) 4b2 - 4bc + c2b - c = (2b)2 - 2 • 2bc + (c)22b - c = (2b- c)2(2b- c) = 2b – c.