ГДЗ по алгебре 7 класс Мерзляк Задание 728

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

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

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

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

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

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

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

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

\[\Longrightarrow тождество\ верно.\]

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

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

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

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

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

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

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

\[\Longrightarrow тождество\ верно.\]