Вправи: 635 (1-3)

635. Спростіть вираз:

1) mn- nm- n = n(m- n)m- n = n;

2) xy- yx- x = y(x- 1)x(x- 1) = yx;

3) 5d+ 5b45d+ 45b = 5(d+ b)45(d+ b) = 19 = 13;

4) cd+ cbad+ ab = c(d+ b)a(d+ b) = ca;

5) xx-x = xx(x- 1) = 1x- 1;

6) a+5aa = a(a+ 5)a = a + 5;

7) 2mm- m = 2mm(m- 1) = 2m-1;

8) 2x+ 2yx+y = 2(x+y)x+y = 2;

9) 8x+ 8y2x+2y = 8(x+ y)2(x+ y = 41 = 2;

10) 3a- 3b27a- 27b = 3(a- b)27(a- b) = 19 = 13;

11) x-1x+ 1 = x- 1(x+ 1)x+ 1 = x – 1;

12) y-4y+ 2 = y- 2(y+ 2)y+ 2 = y – 2;

13) m- 5m-25 = m- 5m- 5(m+ 5) = 1m+ 5;

14) x2- 3x- 3 = x- 3(x+ 3)x- 3 = x + 3;

15) a2- 5a+ 5 = a- 5(a+ 5)a+ 5 = a – 5;

16) m2- 1010- m = m- 10(m+ 10)10- m = –m- 10(m+ 10)m- 10 = –m – 10;

17) x-7x- 7 = x-7(x+ 7)x- 7 = x + 7;

18) a+ 6a-6 = a- 6a- 6(a+ 6) = 1a- 6;

19) m-11m+ 11 = m- 11(m+ 11)m+ 11 = m – 11.

20) mn-m + nm- n = mn- m – nn- m = m-nn- m = –m- n(m+ n)m- n = –m – n;

21) mmn+ n – nmn+ m = m\mn(m+ n) – n\nm(n+ m) = m-nmn(m+ n) = m- n(m+ n)mn(m+ n) = m- nmn.