8. Разложите на множители: 1) 6а³ - 6а; 2) 5х³ - 5ху²; 3) 8а²b² - 72а²с⁸; 4) 3х² - 48ху + 192y²; 5) -8а³ + 8а² - 2а; 6) 5а³ - 40b⁶; 7) a - 3b + a² - 9b²; 8) ac⁴ - c⁴ - ac² + c².

Решение:

1. \( 6a^3 - 6a = 6a(a^2 - 1) = 6a(a-1)(a+1) \)
2. \( 5x^3 - 5xy^2 = 5x(x^2 - y^2) = 5x(x-y)(x+y) \)
3. \( 8a^2b^2 - 72a^2c^8 = 8a^2(b^2 - 9c^8) = 8a^2(b - 3c^4)(b + 3c^4) \)
4. \( 3x^2 - 48xy + 192y^2 = 3(x^2 - 16xy + 64y^2) = 3(x - 8y)^2 \)
5. \( -8a^3 + 8a^2 - 2a = -2a(4a^2 - 4a + 1) = -2a(2a-1)^2 \)
6. \( 5a^3 - 40b^6 = 5(a^3 - 8b^6) = 5(a - 2b^2)(a^2 + 2ab^2 + 4b^4) \)
7. \( a - 3b + a^2 - 9b^2 = (a^2 - 9b^2) + (a - 3b) = (a - 3b)(a + 3b) + (a - 3b) = (a - 3b)(a + 3b + 1) \)
8. \( ac^4 - c^4 - ac^2 + c^2 = c^4(a - 1) - c^2(a - 1) = (a - 1)(c^4 - c^2) = (a - 1)c^2(c^2 - 1) = (a - 1)c^2(c - 1)(c + 1) \)