Решебник по алгебре 7 класс Мерзляк Задание 1168

\[\boxed{\text{1168\ (1168).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ \text{xm} - \text{xn} + \text{ym} - \text{yn} =\]

\[= x \cdot (m - n) + y \cdot (m - n) =\]

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

\[2)\ 3a - 3b + ac - bc =\]

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

\[= (a - b)(3 + c)\]

\[3)\ 9a - ab - 9 + b =\]

\[= a \cdot (9 - b) - (9 - b) =\]

\[= (9 - b)(a - 1)\]

\[4)\ a^{5} + a^{3} + 2a^{2} + 2 =\]

\[= a^{3} \cdot \left( a^{2} + 1 \right) + 2 \cdot \left( a^{2} + 1 \right) =\]

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

\[5)\ 6ab^{2} - 3b^{2} + 2a^{2}b - ab =\]

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

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

\[= b(3b + a)(2a - 1)\]

\[6)\ 2c^{3} - 5c^{2}d - 4c + 10d =\]

\[= 2c \cdot \left( c^{2} - 2 \right) - 5d \cdot \left( c^{2} - 2 \right) =\]

\[= \left( c^{2} - 2 \right)(2c - 5d)\]

\[7)\ x^{3}y^{2} - x + x^{2}y^{3} - y =\]

\[= x \cdot \left( x^{2}y^{2} - 1 \right) + y \cdot \left( x^{2}y^{2} - 1 \right) =\]

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

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

\[8)\ ax^{2} - ay - cy + bx^{2} + cx^{2} - by =\]

\[= x^{2} \cdot (a + b + c) - y \cdot (a + b + c) =\]

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