ГДЗ Алгебра 7 клас Мерзляк (2024)

Розкладіть на множники:

1) x2(x – 2) – 18x(x – 2) + 81(x – 2) = (x – 2)(x2 – 18x + 81) = (x – 2)(x – 9)2;
2) 4x(y2 – 9) + 4x2(y2 – 9) – 9 + y2 = 4x(y2 – 9) + 4x2(y2 – 9) + y2 – 9 = (y2 – 9)(4x + 4x2 + 1) = (y – 3)(y + 3)(2x + 1)2;
3) b2(a + 1) – a2(b + 1) = ab2 + b2 – a2b – a2 = (ab2 – a2b) + (b2– a2) = ab(b – a) + (b – a)(b + a) = (b – a)(ab + b + a);
4) (a – b)(b2 – c2) – (b – c)(a2 – b2) = (a – b)(b – c)(b + c) – (b – c)(a – b)(a + b) = (a – b)(b – c)(b + c – a – b) = (a – b)(b – c)(c– a).