ГДЗ Алгебра 7 клас Мерзляк (2024)

Розкладіть на множники тричлен, виділивши попередньо квадрат двочлена:

1) x2 – 10x + 24 = (x2 – 10x + 25) – 1 = (x – 5)2 – 1 = (x – 5 – 1) ∙ (x – 5 + 1) = (x – 6)(x – 4);
2) a2 + 4a – 32 = (a2 + 4a + 4) – 36 = (a + 2)2 – 36 = (a + 2 – 6)(a + 2 + 6) = (a – 4)(a + 8);
3) b2 – 3b – 4 = (b2 – 3b + 2,25) – 6,25 = (b – 1,5)2 – 6,25 = (b – 1,5 – 2,25)(x – 1,5 + 2,25) = (b – 3,75)(x + 0,75);
4) 4a2 – 12a + 5 = (4a2 – 12a + 9) – 4 = (2a – 3)2 – 22 = (2a – 3 – 2)(2a – 3 + 2) = (2a – 5)(2a – 1);
5) 9x2 – 24xy + 7y2 = (9x2 – 24xy + 16y2) – 9y2 = (3x – 4y)2 – 9y2 = (3x – 4y – 3y)(3x – 4y + 3y) = (3x – 7y)(3x – y);
6) 36m2 – 60mn + 21n2 = (36m2 – 60mn + 25n2) – 4n2 = (6m – 5n)2 – 4n2 = (6m – 5n – 2n)(6m – 5n + 2n) = (6m – 7n)(6m – 3n) = 3(6m – 7n)(2m – n).