9. Разложите многочлен на множители:

Решение:

1. \( 5x^2 - 5y^2 = 5(x^2 - y^2) = 5(x-y)(x+y) \)
2. \( am^2 - an^2 = a(m^2 - n^2) = a(m-n)(m+n) \)
3. \( 2ax^2 - 2ay^2 = 2a(x^2 - y^2) = 2a(x-y)(x+y) \)
4. \( 9p^2 - 9 = 9(p^2 - 1) = 9(p-1)(p+1) \)
5. \( 16x^2 - 4 = 4(4x^2 - 1) = 4(2x-1)(2x+1) \)
6. \( 75 - 27c^2 = 3(25 - 9c^2) = 3(5-3c)(5+3c) \)
7. \( 3xy^2 - 27x = 3x(y^2 - 9) = 3x(y-3)(y+3) \)
8. \( 100ac^2 - 4a = 4a(25c^2 - 1) = 4a(5c-1)(5c+1) \)

Ответ: 1) \( 5(x-y)(x+y) \); 2) \( a(m-n)(m+n) \); 3) \( 2a(x-y)(x+y) \); 4) \( 9(p-1)(p+1) \); 5) \( 4(2x-1)(2x+1) \); 6) \( 3(5-3c)(5+3c) \); 7) \( 3x(y-3)(y+3) \); 8) \( 4a(5c-1)(5c+1) \).