ГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1036

\[\boxed{\text{1036.}\text{\ }еуроки - ответы\ на\ пятёрку}\]

\[\textbf{а)}\ x³ + y³ + 2x² - 2xy + 2y^{2} =\]

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

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

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

\[\textbf{б)}\ a³ - b^{3} + 3a^{2} + 3ab + 3b^{2} =\]

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

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

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

\[\textbf{в)}\ a^{4} + ab³ - a^{3}b - b^{4} =\]

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

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

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

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

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

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

\[\textbf{г)}\ x^{4} + x³y - xy^{3} - y^{4} =\]

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

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

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

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