Решебник по алгебре 7 класс Мерзляк Задание 729

\[\boxed{\text{729\ (729).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ \left( \text{ab} + 1 \right)^{2} - (a + b)^{2} =\]

\[= (\text{ab} + 1 - a - b)(\text{ab} + 1 + a + b)\]

\[\textbf{б)}\ \left( \text{ab} + 1 \right)^{2} - (a + b)^{2} =\]

\[a^{2}b^{2} + 2ab + 1 - a^{2} - 2ab - b^{2} =\]

\[= a^{2}b^{2} - a^{2} + 1 - b^{2} =\]

\[= a^{2}\left( b^{2} - 1 \right) - \left( b^{2} - 1 \right) =\]

\[= \left( b^{2} - 1 \right)\left( a^{2} - 1 \right) =\]

\[= (b - 1)(b + 1)(a - 1)(a + 1)\]

\[\textbf{а)}\ (a + 2b)^{2} - (ab + 2)^{2} =\]

\[= (a + 2b - ab - 2)(a + 2b + ab + 2)\]

\[\textbf{б)}\ (a + 2b)^{2} - (ab + 2)^{2} =\]

\[= (1 - b)(1 + b)(a - 2)(a + 2)\]