ГДЗ по алгебре 7 класс Макарычев Задание 791

\[\boxed{\text{791\ (791).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[\textbf{а)}\ a^{3} - 2a^{2} + 2a - 4 =\]

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

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

\[\textbf{б)}\ x^{3} - 12 + 6x^{2} - 2x =\]

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

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

\[\textbf{в)}\ c^{4} - 2c^{2} + c^{3} - 2c =\]

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

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

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

\[\textbf{г)} - y^{6} - y^{5} + y^{4} + y^{3} =\]

\[= - y^{5}(y + 1) + y^{3}(y + 1) =\]

\[= (y + 1)\left( y^{3} - y^{5} \right) =\]

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

\[\textbf{д)}\ a^{2}b - b^{2}c + a^{2}c - bc^{2} =\]

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

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

\[\textbf{е)}\ 2x^{3} + xy^{2} - 2x^{2}y - y^{3} =\]

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

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

\[\textbf{ж)}\ 16ab^{2} - 10c^{3} + 32ac^{2} - 5b^{2}c =\]

\[= 16a\left( b^{2} + 2c^{2} \right) - 5c\left( 2c^{2} + b^{2} \right) =\]

\[= (2c^{2} + b^{2})(16a - 5c)\]

\[\textbf{з)}\ 6a^{3} - 21a^{2}b + 2ab^{2} - 7b^{3} =\]

\[= 2a\left( 3a^{2} + b^{2} \right) - 7b\left( 3a^{2} + b^{2} \right) =\]

\[= (3a^{2} + b^{2})(2a - 7b)\]