Решебник по алгебре 7 класс Мерзляк Задание 721

\[\boxed{\text{721\ (721).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ a² - b^{2} - a - b =\]

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

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

\[2)\ x - y - x^{2} + y^{2} =\]

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

\[= (x - y)(1 - x - y)\]

\[3)\ 4m² - 9n^{2} + 2m + 3n =\]

\[= (2m + 3n)(2m - 3n + 1)\]

\[4)\ c² - d^{2} + 4c - 4d =\]

\[= (c - d)(c + d) + 4 \cdot (c - d) =\]

\[= (c - d)(c + d + 4)\]

\[5)\ 5x²y - 5xy^{2} - x^{2} + y^{2} =\]

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

\[= (x - y)(5xy - x - y)\]

\[6)\ a² - 10a + 25 - ab + 5b =\]

\[= (a - 5)^{2} - b(a - 5) =\]

\[= (a - 5)(a - 5 - b)\]

\[7)\ 8mp + 8np - m^{2} - 2mn - n^{2} =\]

\[= 8p(m + n) - (m + n)^{2} =\]

\[= (8p - m - n)(m + n)\ \]

\[8)\ a³ + b³ - a^{2}b - ab^{2} =\]

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

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

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

\[9)\ m³ - 8n^{3} - m^{2} + 4mn - 4n^{2} =\]

\[10)\ a³ - 4a^{2} + 4a - 1 =\]

\[= \left( a^{3} - 1 \right) - 4a(a - 1) =\]

\[= (a - 1)\left( a^{2} + a + 1 \right) - 4a(a - 1) =\]

\[= (a - 1)\left( a^{2} + a + 1 - 4a \right) =\]

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