ГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1035

\[\boxed{\text{1035.}\text{\ }еуроки - ответы\ на\ пятёрку}\]

\[\textbf{а)}\ x³ + y³ + 2xy(x + y) =\]

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

\[+ 2xy(x + y) =\]

\[= (x + y)\]

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

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

\[\textbf{б)}\ x³ - y^{3} - 5x\left( x^{2} + xy + y^{2} \right) =\]

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

\[- 5x\left( x^{2} + xy + y^{2} \right) =\]

\[= \left( x^{2} + xy + y^{2} \right)(x - y - 5x) =\]

\[= (x^{2} + xy + y^{2})( - 4x - y)\]

\[\textbf{в)}\ 2b³ + a\left( a^{2} - 3b^{2} \right) = 2b³ +\]

\[+ a^{3} - 3ab^{2} = a^{3} - b^{3} +\]

\[+ 3b^{3} - 3ab^{2} =\]

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

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

\[= (a - b)\]

\[\left( a^{2} + ab + b^{2} - 3b^{2} \right) =\]

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

\[\textbf{г)}\ p³ - 2p^{2} + 2p - 1 =\]

\[= (p - 1)\left( p^{2} + p + 1 \right) -\]

\[- 2p(p - 1) =\]

\[= (p - 1)\left( p^{2} + p + 1 - 2p \right) =\]

\[= (p - 1)(p^{2} - p + 1)\]

\[\textbf{д)}\ 8b³ + 6b² + 3b + 1 =\]

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

\[+ 3b(2b + 1) =\]

\[= (2b + 1)\]

\[\left( 4b^{2} - 2b + 1 + 3b \right) =\]

\[= (2b + 1)(4b^{2} + b + 1)\]

\[\textbf{е)}\ a³ - 4a^{2} + 20a - 125 =\]

\[= (a - 5)\left( a^{2} + 5a - 25 \right) -\]

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

\[= (a - 5)\left( a^{2} + 5a + 25 - 4a \right) =\]

\[= (a - 5)(a^{2} + a + 25)\]