ГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1034

\[\boxed{\text{1034.}\text{\ }еуроки - ответы\ на\ пятёрку}\]

\[\textbf{а)}a² + b² - 2ab - 25 =\]

\[= (a - b)^{2} - 25 =\]

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

\[\textbf{б)}\ 36 - b^{2} - c^{2} + 2bc = 36 -\]

\[- \left( b^{2} - 2bc + c^{2} \right) = 36 -\]

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

\[= (6 - b + c)(6 + b - c)\]

\[\textbf{в)}\ 49 - 2ax - a^{2} - x^{2} = 49 -\]

\[- \left( a^{2} + 2ax + x^{2} \right) = 7^{2} -\]

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

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

\[\textbf{г)}\ b² - a^{2} - 12a - 36 = b^{2} -\]

\[- \left( a^{2} + 12a + 36 \right) = b^{2} -\]

\[- (a + 6)^{2} =\]

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

\[\textbf{д)}\ 81a² + 6bc - 9b^{2} - c^{2} =\]

\[= 81a^{2} - \left( 9b^{2} - 6bc + c^{2} \right) =\]

\[= 81a^{2} - (3b - c)^{2} =\]

\[= (9a - 3b + c)(9a + 3b - c)\]

\[\textbf{е)}b²c² - 4bc - b^{2} - c^{2} + 1 =\]

\[= b^{2}c^{2} - 2bc + 1 -\]

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

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

\[= (bc - 1 - b - c)\]

\[(bc - 1 + b + c)\ \]