ГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1005

\[\boxed{\text{1005.}\text{\ }еуроки - ответы\ на\ пятёрку}\]

\[\textbf{а)}\ (x + 1)^{3} + x³ =\]

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

\[- x(x + 1) + x²) =\]

\[= (2x + 1)\]

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

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

\[\textbf{б)}\ (y - 2)^{3} - 27 =\]

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

\[\left( (y - 2)^{2} + 3 \cdot (y - 2) + 9 \right) =\]

\[= (y - 5)\]

\[\left( y^{2} - 4y + 4 + 3y - 6 + 9 \right) =\]

\[= (y - 5)(y^{2} - y + 7)\]

\[\textbf{в)}\ (a - b)^{3} + b³ =\]

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

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

\[= a\]

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

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

\[\textbf{г)}\ 8x³ + (x - y)^{3} =\]

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

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

\[= (3x - y)\]

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

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

\[\textbf{д)}\ 27a³ - (a - b)^{3} =\]

\[= \left( 3a - (a - b) \right)\]

\[\left( 9a^{2} + 3a(a - b) + (a - b)^{2} \right) =\]

\[= (2a + b)\]

\[\left( 9a^{2} + 3a^{2} - 3ab + a^{2} - 2ab + b^{2} \right) =\]

\[= (2a + b)(13a^{2} - 5ab + b^{2})\]

\[\textbf{е)}\ 1000 + (b - 8)^{3} =\]

\[= (10 + b - 8)\]

\[\left( 100 - 10 \cdot (b - 8) + (b - 8)^{2} \right) =\]

\[= (2 + b)\]

\[\left( 100 - 10b + 80 + b^{2} - 16b + 64 \right) =\]

\[= (2 + b)(b^{2} - 26b + 244)\]