ГДЗ Алгебра 7 клас Мерзляк (2024)

Подайте у вигляді добутку вираз:

1) x2(x + 4) – 20x(x + 4) + 100(x + 4) = (x + 4)(x2 –20x + 100) = (x + 4)(x – 10)2;
2) a2 – 36 – 2a(36 – a2) – a2(36 – a2) = a2 – 36 + 2a(a2 – 36) + a2(a2 – 36) = (a2 – 36)(1 + 2a + a2) = (a – 6)(a + 6)(1 + a)2;
3) a2(b – 1) – b2(a – 1) = a2b – a2 – ab2 + b2 = (a2b – ab2) – (a2 – b2) = ab(a – b) – (a – b)(a + b) = (a – b)(ab – a – b);
4) (m – n)(n3 – p3) – (n – р)(m3 – n3) = (m – n)(n – p)(n2 + np + p2) – (n – p)(m – n)(m2 + mn + n2) = (m – n)(n – p)(n2 + np + p2 – m2 – mn – n2) = (m – n)(n – p)(np + p2 – m2 – mn) = (m – n)(n – p)((np – mn) + (p2 – m2)) = (m – n)(n – p)(n(p – m) + (p – m)(p + m)) = (m – n)(n – p)(p – m)(n + p + m).