Вправи: 536 (1-4)

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;