Вправи: 537

537. Спростіть вираз:

1) a- 3a+ 1 – a- 4a = aa- 3- (a- 4)(a+ 1)a(a+ 1) = a-3a- (a+ a- 4a- 4)a(a+ 1) = a-3a- a+4a- a+ 4a(a+ 1) = 4a+ a;

2) a+ 1a- ab – b+ 1ab- b = a+ 1(a)2- ab – b+ 1ab- (b)2 = a+ 1\ba(a- b) – b+ 1\ab(a- b) = ab+ b- ab- aab(a- b) = -(a- b)ab(a- b) = –1ab;

3) xy-2y : x3y-6 = x • 3(y- 2)yy- 2 • x = 3y;

4) mm- n : (m+ nn + nm- n) = nm.

1. m+ n\m-nn+ n\nm- n = (m)2- (n)2+ (n)2n(m- n) = m-n+nn(m- n) = mn(m- n);

2. mm- n : mn(m- n) = m • n(m- n)m- n • n = m • n(m)2 = nm = nm;

5) (x+ 1x- 1 – 4xx-1) • x+ xx- 1 = x.

1. x+ 1\x+1x- 1 – 4xx- 1(x+ 1) = (x+ 1)2- 4xx- 1(x+ 1) = x+2x +1-4xx- 1(x+ 1) = x-2x +1x- 1(x+ 1) = (x- 1)2x- 1(x+ 1) = x- 1x+ 1;

2. x- 1x+ 1 : x+ xx- 1 = x- 1 • xx+ 1x+ 1(x- 1) = x;

6) a-64a+ 3 • 1a+8a – a+ 8a-3a = a-64 • 1a+ 3 • a(a+ 8) – a+ 8a(a- 3) = a- 8(a+ 8)a+ 3 • a(a+ 8) – a+ 8a(a- 3) = a- 8a(a+ 3) – a+ 8a(a- 3) = a- 8a- 3- (a+ 8)(a+ 3)aa+ 3(a-3a) = a-3a- 8a+ 24-a-8a- 3a- 24aa+ 3(a- 3) = -22aaa+ 3(a- 3) = -22a(a)2- 32 = -22a-9 = 229 -a.