ГДЗ Алгебра 7 клас Мерзляк (2024)

Подайте у вигляді добутку многочлен:

1) 3аb + 15b – 3a – 15 = 3b(a + 5) – 3(a + 5) = (a + 5)(3b – 3);
2) 84 – 42y – 7xy + 14x = 42(2 – y) + 7x(2 – y) = (2 – y)(42 + 7x);
3) abc + 6ac + 8ab + 48а = ac(b + 6) + 8a(b + 6) = (b + 6)(ac + 8a);
4) m3 – m2n + m2 – mn = m(m2 – mn + m – n) = m(m(m – n) + (m – n)) = m(m – n)(m + 1);
5) a3 + а2 – a – 1 = a2(a + 1) – (a + 1) = (a + 1)(a2 – 1) = (a + 1)(a – 1)(a + 1) = (a – 1)(a + 1)2;
6) 2x3 – 2хy2 – 8x2 + 8y2 = 2x(x2 – y2) – 8(x2 – y2) = (x2 – y2)(2x – 8) = 2(x – y)(x + y)(x – 4);
7) 5a2 – 5b2 – 15a3b + 15ab3 = 5(a2 – b2) – 15ab(a2 – b2) = (a2 – b2)(5 – 15ab) = 5(a – b)(a + b)(1 – 3аb);
8) a2b2 – 1 – b2 + a2 = a2b2 – b2 + a2 – 1 = b2(a2 – 1) + (a2 – 1) = (a2 – 1)(b2 + 1) = (a – 1)(a + 1)(b2 + 1).