Решебник по алгебре 7 класс Мерзляк ФГОС Задание 728

 

\[\boxed{\text{728\ (728).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ (a + 2)^{3} - 25 \cdot (a + 2) =\]

\[= (a + 2)(a + 7)(a - 3)\]

\[(a + 2)^{3} - 25 \cdot (a + 2) =\]

\[= (a + 2)\left( (a + 2)^{2} - 25 \right) =\]

\[= (a + 2)(a + 2 - 5)(a + 2 + 5) =\]

\[= (a + 2)(a - 3)(a + 7)\]

\[(a + 2)(a - 3)(a + 7) =\]

\[= (a + 2)(a - 3)(a + 7) \Longrightarrow\]

\[\Longrightarrow тождество\ верно.\]

\[2)\ a² + 2ab + b² - c^{2} + 2cd - d^{2} =\]

\[= (a + b + c - d)(a + b - c + d)\]

\[a^{2} + 2ab + b^{2} - c^{2} + 2cd - d^{2} =\]

\[= (a + b)^{2} - (c - d)^{2} =\]

\[= (a + b - c + d)(a + b + c - d)\]

\[(a + b - c + d)(a + b + c - d) =\]

\[= (a + b - c + d)(a + b + c - d) \Longrightarrow\]

\[\Longrightarrow тождество\ верно.\]

\[\boxed{\text{728.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[рис.\ 5:(a + b)(a + b) =\]

\[= a^{2} + \text{ab} + \text{ba} + b^{2} =\]

\[= a² + 2\text{ab} + b² = (a + b)^{2};\]

\[рис.\ 6:(a - b)(a - b) =\]

\[= a^{2} - ab - ba + b^{2} =\]

\[= a^{2} - 2ab + b^{2} = (a - b)²\]