Вправи: 151

151. Спростіть вираз:

1) 7a2a2- 25 • 5-aa = -7a2(a-5)a-5a+5 • a = –7aa+5;

2) a3+ b3a3- b3 • b-ab+a = a+ba2- ab+ b2 • (-a-b)a-ba2+ ab+ b2 • (b+a) = –a2- ab+ b2a2+ ab+ b2;

3) a4- 1a3- a • a1+ a2 = a2- 1a2+ 1 • aaa2- 1(a2+ 1) = 1;

4) a2- 8ab12b : 8b2- ab24a = aa-8b • 24a12b-b(a-8b) = 2a2-b2 = –2a2b2;

5) a4- 1a2- a+1 : (a-1)a3+ 1 = a-1a+1a2+ 1 • a+1(a2- a+1)a2- a+1(a-1) = (a + 1)²(a² + 1);

6) 4x2- 1006x : 2x2- 20x+501 = 4x-5x+5 • 16x • 2(x-5)2 = x+53x(x-5) = x+53x2- 15x.