Решебник по алгебре 9 класс Макарычев Задание 88

 

\[\boxed{\text{88\ (88).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ 4x^{2} - 6x + 2xy - 3y =\]

\[= 2x(2x - 3) + y(2x - 3) =\]

\[= (2x - 3)(2x + y).\]

\[\textbf{б)}\ 4a^{3} + 2b^{3} - 2a^{2}b - 4ab^{2} =\]

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

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

\[= 2 \cdot (2a - b)(a - b)(a + b)\]

\[\boxed{\text{88.\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[\textbf{а)}\ \frac{2a - 7b + 5}{7a - 2b + 5} = 9\]

\[2a - 7b + 5 = 9 \cdot (7a - 2b + 5)\]

\[2a - 7b + 5 = 63a - 18b + 45\]

\[61a - 11b + 40 = 0\]

\[61a - 11b + 50 = 10\]

\[Ответ:10.\]

\[\textbf{б)}\ \frac{a}{b} = 3;\ \ a = 3b:\]

\[\frac{a + 9b + 16}{a + 3b + 8} = \frac{3b + 9b + 16}{3b + 3b + 8} =\]

\[= \frac{12b + 16}{6b + 8} = \frac{2 \cdot (6b + 8)}{6b + 8} = 2.\]

\[Ответ:2.\]

\[\textbf{в)}\ \frac{3a - 7b + 4}{7a - 3b + 4} = 9\]

\[3a - 7b + 4 = 9 \cdot (7a - 3b + 4)\]

\[3a - 7b + 4 = 63a - 27b + 36\]

\[60a - 20b + 32 = 0\ \ \ |\ :2\]

\[30a - 10b + 16 = 0\]

\[30a - 10b - 13 = - 29\]

\[Ответ:\ - \ 29.\]

\[\textbf{г)}\ \frac{a}{b} = 4;\ \ a = 4b:\]

\[\frac{a + 11b + 51}{a + b + 17} =\]

\[= \frac{4b + 11b + 51}{4b + b + 17} = \frac{15b + 51}{5b + 17} =\]

\[= \frac{3 \cdot (5b + 17)}{5b + 17} = 3.\]

\[Ответ:3.\]