ГДЗ Алгебра 7 клас Тарасенкова (2024)

Розкладіть на множники многочлен:
1) Зx3 – Зху2 = 3x(x2 – y2) = 3x(x – y)(x + y);
2) 25а3b – 16аb3 = ab(25a2 – 16b2) = ab(5a – 4b)(5a + 4b);
3) 5с2d2 – 125c4d4 = 5c2d2(1 – 25c2d2) = 5c2d2(1 – 5cd)(1 + 5cd);
4) 18m4n2 – 162m2n4 = 18m2n2(m2 – 9n2) = 18m2n2(m – 3n)(m + 3n);
5) ас3 – аb3 = a(c3 – b3) = a(c – b)(c2 + ab + b2);
6) –8mn3 – 27md3 = 8mn3 + 27md3 = m(8n3 + 27d3) = m(2n + 3d)(4n2 – 6nd + 9d2);
7) 7az4 – 56a4z = 7az(z3 – 8a3) = 7az(z – 2a)(z2 + 2az + 4a2);
8) х3у3 + 64х6у6 = (xy + 4x2y2)(x2y2 – 4x3y3 + 16x4y4);
9) За2b – 6аb2 + 3b3 = 3b(a2 – 2ab + b2) = 3b(a – b)2;
10) 7x3 – 14х2у + 7ху2 = 7x(x2 – 2xy + y2) = 7x(x – y)2;
11) а2 – 2ab + b2 – с2 = (a – b)2 – c2 = (a – b – c)(a – b + c);
12) 9 – c2 – 4mс – 4m2 = c2 + 4mc + 4m2 – 9 = (c + 2m) – 9 = (c + 2m – 3)(c + 2m + 3).