ГДЗ Алгебра 8 клас Істер (2025)

Розкладіть многочлен на множники:

1) 6а^3 – 2а^2 – 12a = 2a(3а^2 – a – 6) = 2a(3a + 2)(a – 3);
2) x^5 – 3x^3 – 2x^2 + 6 = (x^5 – 3x^3) – (2x^2 – 6) = x^3(x^2 – 3) – 2(x^2 – 3) = (x^2 – 3)( x^3 – 2);
3) –4x^2 + 20x – 25 = –(4x^2 – 20x + 25) = –〖(2x-5)〗^2;
4) 0,36p^8 – c^10 x^12 = 〖(0,6p^4)〗^2 – 〖(c^5 x^6)〗^2 = (0,6p^4 – c^5 x^6)(0,6p^4 + c^5 x^6);
5) 64m^3 c^9 + t^30 = 〖(4mc^3)〗^3 + 〖(t^10)〗^3 = (4mc^3 + t^10)(〖(4mc^3)〗^2 – 4mc^3 • t^10 + t^20) = (4mc^3 + t^10)(16m^2 c^6 – 4mc^3 t^10 + t^20);
6) c^2 + 2cd + d^2 – 25 = 〖(c+d)〗^2 – 5^2 = ((c + d) – 5)((c + d) + 5).