Решебник по алгебре 7 класс Мерзляк Задание 717

\[\boxed{\text{717\ (717).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ 3\text{ab} + 15b - 3a - 15 =\]

\[= 3a(b - 1) + 15 \cdot (b - 1) =\]

\[= (b - 1)(3a + 15) =\]

\[= 3 \cdot (a + 5)(b - 1)\]

\[2)\ 84 - 42y - 7xy + 14x =\]

\[= 42 \cdot (2 - y) + 7x( - y + 2) =\]

\[= (2 - y)(42 + 7x) =\]

\[= 7 \cdot (2 - y)(6 + x)\]

\[3)\ abc + 6ac + 8ab + 48a =\]

\[= ac(b + 6) + 8a(b + 6) =\]

\[= (b + 6)(ac + 8a) =\]

\[= a \cdot (c + 8)(b + 6)\]

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

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

\[= (m - n)\left( m^{2} + m \right) =\]

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

\[5)\ a³ + a² - a - 1 =\]

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

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

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

\[6)\ 2x³ - 2xy^{2} - 8x^{2} + 8y^{2} =\]

\[= 2x\left( x^{2} - y^{2} \right) - 8 \cdot \left( x^{2} - y^{2} \right) =\]

\[= (2x - 8)\left( x^{2} - y^{2} \right) =\]

\[= 2 \cdot (x - 4)(x - y)(x + y)\]

\[7)\ 5a² - 5b^{2} - 15a^{3}b + 15ab^{3} =\]

\[= 5 \cdot \left( a^{2} - b^{2} \right) - 15ab\left( a^{2} - b^{2} \right) =\]

\[= 5 \cdot (1 - 3ab)(a - b)(a + b)\]

\[8)\ a²b² - 1 - b^{2} + a^{2} =\]

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

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

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