Решебник по алгебре 7 класс Мерзляк Задание 719

\[\boxed{\text{719\ (719).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

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

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

\[= (a - b)²(a + b)²\]

\[2)\ 81 - \left( x^{2} + 6x \right)^{2} =\]

\[= \left( 9 - x^{2} - 6x \right)\left( 9 + x^{2} + 6x \right) =\]

\[= (9 - x^{2} - 6x)(x + 3)²\]

\[3)\ a² + 2ab + b² - c^{2} =\]

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

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

\[4)\ c² + 4c + 4 - k^{2} =\]

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

\[= (c + 2 - k)(c + 2 + k)\]

\[5)\ 9a² + c² + 6ac - 9 =\]

\[= (3a + c)^{2} - 9 =\]

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

\[6)\ a² - b^{2} - 10b - 25 =\]

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

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

\[7)\ 49 - y^{2} + x^{2} - 14x =\]

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

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

\[8)\ mn² - m^{3} - 12m^{2} - 36m =\]

\[= m\left( n^{2} - m^{2} - 12m - 36 \right) =\]

\[= m\left( n^{2} - (m + 6)^{2} \right) =\]

\[= m(n - m - 6)(n + m + 6)\]