Вправи: 536

536. Спростіть вираз:

1) aa- 2 – 4a- 4a- 2 = a-(4a- 4)a- 2 = (a)2- 2 • 2a+ 22a- 2 = (a- 2)2a- 2 = a – 2;

2) m+ 1\mm- 2 – m+ 3\m- 2m = (m)2+ m- ((m)2- 2m+ 3m- 6)m(m- 2) = m+ m- m+2m- 3m+ 6m(m- 2) = 6m(m- 2) = 6m-2m;

3) y+ 4xy+ y – x- 4x+ xy = y+ 4xy+ (y)2 – x- 4(x)2+ xy = y+ 4\xxy+ y – x- 4\yx+ xy = xy+ 4x- xy+ 4yxy(x+ y) = 4(x+ y)xy(x+ y) = 4xy;

4) aa+ 4 – aa-16 = a\a- 4a+ 4 – aa+ 4(a- 4) = (a)2- 4a- aa+ 4(a- 4) = a-4a- aa+ 4(a- 4) = –4aa-16 = 4a16-a;

5) aab- b + bb- a = aab- (b)2 + bb- a = aba- b – b\b(a- b) = a-(b)2b(a- b) = (a)2- (b)2b(a- b) = a- b(a+ b)b(a- b) = a+ bb;

6) a+ ab • b2a+ 2 = (a)2+ ab • (b)22a+ 2 = aa+ 1 • (b)2b(a+ 1) = ab2;

7) c- 5c : c-253x = c- 5•3cc •(c-25) = c- 5•3(c)2cc- 5(c+ 5) = 3cc+ 5;

8) (a\a+1 – aa+ 1) : aa-1 = (a)2+ a- aa+ 1 : aa-1 = a+ a- a • (a-1)a+ 1 • a = a • a- 1(a+ 1)a+ 1 • a = a – 1;

9) (a+ bb + ba- b) : ab = a+ ba- b+ (b)2b(a- b) : ab = a-b+b • bba- b • a = a(a- b)a = (a)2(a- b)a = aa- b;

10) (x- 3x+ 3 + 12xx-9) : x+ 3x-3x = x.

1. x- 3\x-3x+ 3 + 12xx- 3(x+ 3) = (x- 3)2+ 12xx- 3(x+ 3) = x-6x+ 9+12xx- 3(x+ 3) = x+6x+ 9x- 3(x+ 3) = (x+ 3)2x- 3(x+ 3) = x+ 3x- 3;

2. x+ 3x- 3 : x+ 3x-3x = x+ 3 • x(x- 3)x- 3(x+ 3) = x.