Решебник по алгебре 7 класс Мерзляк Задание 734

\[\boxed{\text{734\ (734).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ x² - 10x + 24 =\]

\[= \left( x^{2} - 10x + 25 \right) - 1 =\]

\[= (x - 5)^{2} - 1 =\]

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

\[= (x - 6)(x - 4)\]

\[2)\ a² + 4a - 32 =\]

\[= \left( a^{2} + 4a + 4 \right) - 36 =\]

\[= (a + 2)^{2} - 36 =\]

\[= (a + 2 - 6)(a + 2 + 6) =\]

\[= (a - 4)(a + 8)\]

\[3)\ b² - 3b - 4 =\]

\[= \left( b^{2} - 3b + 2,25 \right) - 6,25 =\]

\[= (b - 1,5)^{2} - 6,25 =\]

\[= (b - 1,5 - 2,5)(b - 1,5 + 2,5) =\]

\[= (b - 4)(b + 1)\]

\[4)\ 4a² - 12a + 5 =\]

\[= \left( 4a^{2} - 12a + 9 \right) - 4 =\]

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

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

\[= (2a - 1)(2a - 5)\]

\[5)\ 9x² - 24xy + 7y^{2} =\]

\[= \left( 9x^{2} - 24xy + 16y^{2} \right) - 9y^{2} =\]

\[= (3x - 4y)^{2} - 9y^{2} =\]

\[= (3x - 4y - 3y)(3x - 4y + 3y) =\]

\[= (3x - 7y)(3x - y)\]

\[6)\ 36m² - 60mn + 21n^{2} =\]

\[= \left( 36m^{2} - 60mn + 25n^{2} \right) - 4n^{2} =\]

\[= (6m - 5n) - 4n^{2} =\]

\[= (6m - 5n - 2n)(6m - 5n + 2n) =\]

\[= (6m - 7n)(6m - 3n) =\]

\[= 3 \cdot (6m - 7n)(2m - n)\]