Вправи: 159

159. 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) 5m2- 5n2m2+ n2 : 15n-15m4m2+ 4n2 = 5m-nm+n • 4(m2+ n2)m2+ n2 • -15 • (m-n) = –4(m+n)3 = –4m+4n3;

6) mn2- 36mm3- 8 : 2n+126m-12 = mn-6n+6 • 6(m-2)m-2m2+ 2m+4 • 2(n+6) = 3m(n-6)m2+ 2m+4 = 3mn-18mm2+ 2m+4;

7) 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);

8) 4x2- 1006x : 2x2- 20x+501 = 4x-5x+5 • 16x • 2(x-5)2 = x+53x(x-5) = x+53x2- 15x.