ГДЗ Алгебра 7 клас Мерзляк (2024)

Розкладіть на множники:

1) (a + 6)3 – 27 = (a + 6)3 – З3 = (a + 6 – 3)((a + 6)2 + 3(a + 6) + 9) = (a + З)(а2 + 12a + З6 + Зa + 18 + 9) = (a + 3)(a2 + 15a + 63);
2) (2x – 1)3 + 64 = (2x – 1)3 + 43 = (2x – 1 + 4)((2x – 1)2 – 4(2x – 1) + 16) = (2x + 3)(4x2 – 4x + 1 – 8x + 4 + 16) = (2x + 3)(4x2 – 12x + 21);
3) 8a6 – (4a – З)3 = (2a2)3 – (4a – З)3 = (2a2 – (4a – 3))((2a2)2 + 2a2(4a – 3) + (4a – 3)2) = (2a2 – 4a + 3)(4a4 + 8a3 – 6a2 + 16a2 – 24a + 9) = (2a2 – 4a + 3)(4a4 + 8a3 + 10a2 – 24a + 9);
4) 1000 + (y – 10)3 = 103 + (y – 10)3 = (10 + y – 10)(102 – 10(y – 10) + (y – 10)2) = y(100 – 10y + 100 + y2 – 20y + 100) = y(y2 – 30y + 300);
5) (x + y)3 – (x – y)3 = (x + y – x + y)((x + y)2 + (x + y)(x – y) + (x – – y)2) = 2y(x2 + 2xy + y2 + x2 – y2 + x2 – 2xy + y2) = 2y(3x2 + y2);
6) (a – 2)3 + (a + 2)3 = (a – 2 + a + 2)((a – 2)2 – (a – 2)(a + 2) + (a + 2)2) = 2a(a2 – 4a + 4 – a2 + 4 + a2 + 4a + 4) = 2a(a2 + 12).