вправа 729 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) a) (ab + 1)² - (a + b)² =
= (ab + 1 - (a + b))(ab + 1 + (a + b)) =
= (ab + 1 - a - b)(ab + 1 + a + b) =
= (a(b - 1) - (b - 1))(a(b + 1) + (b + 1)) =
= (a - 1)(b - 1)(a + 1)(b + 1);
б) (ab + 1)² - (a + b)² =
= a²b² + 2ab + 1 - a² - 2ab - b² =
= a²b² + 1 - a² - b² =
= b²(a² - 1) - (a² - 1) =
= (a² - 1)(b² - 1) =
= (a + 1)(a - 1)(b + 1)(b - 1);
2) a) (a + 2b)² - (ab + 2)² =
= (a + 2b - (ab + 2))(a + 2b + (ab + 2)) =
= (a + 2b - ab - 2)(a + 2b + ab + 2) =
= ((a - 2) - b(a - 2))((a + 2) + b(a + 2)) =
= (a - 2)(1 - b)(a + 2)(1 + b);
б) (a + 2b)² - (ab + 2)² =
= a² + 4ab + 4b² - a²b² - 4ab - 4 =
= a² + 4b² - a²b² - 4 =
= (a² - 4) - b²(a² - 4) =
= (a² - 4)(1 - b²) =
= (a - 2)(a + 2)(1 - b)(1 + b).