ГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1033

\[\boxed{\text{1033.}\text{\ }еуроки - ответы\ на\ пятёрку}\]

\[\textbf{а)}\ a² - b^{2} + 2 \cdot (a + b)^{2} =\]

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

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

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

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

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

\[\textbf{б)}\ b² - c^{2} - 10 \cdot (b - c)^{2} =\]

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

\[- 10 \cdot (b - c)^{2} =\]

\[= (b - c)\left( b + c - 10 \cdot (b - c) \right) =\]

\[= (b - c)(b + c - 10b + 10c) =\]

\[= (b - c)(11c - 9b)\]

\[\textbf{в)}\ 2 \cdot (x - y)^{2} + 3x² - 3y^{2} =\]

\[= 2 \cdot (x - y)^{2} + 3 \cdot \left( x^{2} - y^{2} \right) =\]

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

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

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

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

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

\[\textbf{г)}\ 5a² - 5 - 4 \cdot (a + 1)^{2} =\]

\[= 5 \cdot \left( a^{2} - 1 \right) - 4 \cdot (a + 1)^{2} =\]

\[= 5 \cdot (a - 1)(a + 1) -\]

\[- 4 \cdot (a + 1)^{2} =\]

\[= (a + 1)\]

\[\left( 5 \cdot (a - 1) - 4 \cdot (a + 1) \right) =\]

\[= (a + 1)(5a - 5 - 4a - 4) =\]

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