Вправи: 837

837. Виконайте ділення:

1) x2- 10x+25x2- 100 : x-5x-10 = (x-5)2 • (x-10)x-10x-10(x-5) = x-5x+10;

2) a2- 1a-8 : a2+ 20+1a-8 = a-1a+1(a-8)a-8(a+1)2 = a-1a+1;

3) ab+ b28b : ab+ a22a = ba+b • a8b • a(a+b) = 14;

4) 2c-3c-1 : (2c – 3) = 2c-3 • 1c-1 • (2c-3) = 1c-1;

5) x2- 16y225x2- 4y2 : x2+ 8xy+16y225x2+ 20xy+4y2 = x-4yx+4y • (5x+2y)25x-2y5x+2y • (x+4y)2 = x-4y(5x+2y)5x-2y(x+4y) = 5x2+ 2xy-20xy-8y25x2+ 20xy-2xy-8y2 = 5x2- 18xy-8y25x2+ 18xy-8y2;

6) n2- 3n49n2- 1 : n4- 27n49n2- 14n+1= nn-3 • (7n-1)27n-17n+1 • nn-3(n2+ 3n+9) = 7n-17n+1(n2+ 3n+9) = 7n-17n3+ 21n2+ 63+ n2+ 3n+9 = 7n-17n3+ 22n2+ 3n+72;

7) m12- n152m10- 8n14 : 5m8+ 5m4n5+ 5n103m5+ 6n7 = m4- n5m8+ m4n5+ n10 • 3(m5+ 2n7)2m5- 2n7m5+ 2n7 • 5(m8+ m4n5+ n10) = 3m4- 3n510m5- 20n7;

8) 5a2- 20ab3a2+ b2: 30(a-4b)29a4- b4 = 5aa-4b • 3a2- b2(3a2+ b2)3a2+ b2• 30(a-4b)2 = a(3a2- b2)6(a-4b)2 = 3a3- ab26a-24b.