ГДЗ Алгебра 7 клас Мерзляк (2024)

Розкладіть на множники многочлен:

1) x2 – 4x + 3 = (x2 – 4x + 4) – 1 = (x – 2)2 – 1 = (x – 2 – 1)(x –2 + 1) = (x – 3)(x – 1);
2) a2 + 2a – 24 = (a2 + 2a + 1) – 25 = (a + 1)2 – 25 = (a + 1 – 5)(a + 1 + 5) = (a – 4)(a + 6);
3) y2 + 12y + 35 = (y2 + 12y + 36) – 1 = (y + 6)2 – 1 = (y + 6 – 1)(y + 6 + 1) = (y + 5)(y + 7);
4) x2 + x – 6 (x2 + x + 0,25) – 6,25 = (x + 0,5)2 – 6,25 = (x + 0,5 – 2,5)(x + 0,5 + 2,5) = (x – 2)(x + 3);
5) c2 + 8cd + 15d2 = (c2 + 8cd + 16d2) – d2 = (c + 4d)2 – d2 = (c + 4d + d) = (c + 3d)(c + 5d);
6) 9x2 – 30xy + 16y2 = (9x2 – 30xy + 25y2) – 9y2 = (3x – 5y)2 – 9y2 = (3x – 5y – 3y)(3x – 5y + 3y) = (3x – 8y)(3x – 2y).