Решебник по алгебре 7 класс Мерзляк Задание 722

\[\boxed{\text{722\ (722).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ m² - n^{2} - m + n =\]

\[= (m - n)(m + n) - (m - n) =\]

\[= (m - n)(m + n - 1)\]

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

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

\[= (c + d)(1 - c + d)\]

\[3)\ 16x² - 25y^{2} - 4x - 5y =\]

\[= (4x - 5y)(4x + 5y) - (4x + 5y) =\]

\[= (4x + 5y)(4x - 5y - 1)\]

\[4)\ 12a²b³ + 3a³b² + 16b² - a^{2} =\]

\[= (4b + a)(3a^{2}b^{2} + 4b - a)\]

\[5)\ 49c² - 14c + 1 - 21ac + 3a =\]

\[= (7c - 1)^{2} - 3a(7c - 1) =\]

\[= (7c - 1)(7c - 1 - 3a)\]

\[6)\ ax² + ay² + x^{4} + 2x²y² + y^{4} =\]

\[= a\left( x^{2} + y^{2} \right) + \left( x^{2} + y^{2} \right)^{2} =\]

\[= \left( x^{2} + y^{2} \right)\left( a + x^{2} + y^{2} \right)\]

\[7)\ 27c³ - d^{3} + 9c^{2} + 3cd + d^{2} =\]

\[= \ \left( 9c^{2} + 3cd + d^{2} \right)(3c - d + 1)\]

\[8)\ b³ - 2b^{2} - 2b + 1 =\]

\[= \left( b^{3} + 1 \right) - 2b(b + 1) =\]

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

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

\[= (b + 1)(b^{2} - 3b + 1)\]