Упростите выражение:
а) (2n + 3)(n + 1) + (4n − 1)(n − 1) + 2;
б)

(2 n^{2} - 1) (n + 1) - (n^{2} + 1) (2 n - 1)

;
в)

((b + c)^{2} - (b^{2} + c^{2}))^{3} - (3 b c)^{3}

;
г)

((m - n)^{2} + 2 m n)^{3} - 3 m^{2} n^{2} (m^{2} + n^{2})

;
д)

((x - y)^{3} + 3 x y (x - y))^{2} + 2 x^{3} y^{3}

;
е)

((y + z)^{3} - (y^{3} + z^{3}))^{2} - 18 y^{3} z^{3}

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ГДЗ учебник по алгебре 7 класс Дорофеев. 7. Дополнительные задания. Номер №795

(2 n + 3) (n + 1) + (4 n - 1) (n - 1) + 2 = 2 n^{2} + 3 n + 2 n + 3 + 4 n^{2} - n - 4 n + 1 + 2 = 6 n^{2} + 6

(2 n^{2} - 1) (n + 1) - (n^{2} + 1) (2 n - 1) = 2 n^{3} - n + 2 n^{2} - 1 - (2 n^{3} + 2 n - n^{2} - 1) = 2 n^{3} - n + 2 n^{2} - 1 - 2 n^{3} - 2 n + n^{2} + 1 = 3 n^{2} - 3 n

((b + c)^{2} - (b^{2} + c^{2}))^{3} - (3 b c)^{3} = (b^{2} + 2 b c + c^{2} - b^{2} - c^{2})^{3} - 27 b^{3} c^{3} = (2 b c)^{3} - 27 b^{3} c^{3} = 8 b^{3} c^{3} - 27 b^{3} c^{3} = - 19 b^{3} c^{3}

((m - n)^{2} + 2 m n)^{3} - 3 m^{2} n^{2} (m^{2} + n^{2}) = (m^{2} - 2 m n + n^{2} + 2 m n)^{3} - 3 m^{4} n^{2} - 3 m^{2} n^{4} = (m^{2} + n^{2})^{3} - 3 m^{4} n^{2} - 3 m^{2} n^{4} = m^{6} + 3 m^{4} n^{2} + 3 m^{2} n^{4} + n^{6} - 3 m^{4} n^{2} - 3 m^{2} n^{4} = m^{6} + n^{6}

((x - y)^{3} + 3 x y (x - y))^{2} + 2 x^{3} y^{3} = (x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3} - 3 x^{2} y - 3 x y^{2})^{2} + 2 x^{3} y^{3} = (x^{3} - y^{3})^{2} + 2 x^{3} y^{3} = x^{6} - 2 x^{3} y^{3} + y^{6} + 2 x^{3} y^{3} = x^{6} + y^{6}

((y + z)^{3} - (y^{3} + z^{3}))^{2} - 18 y^{3} z^{3} = (y^{3} + 3 y^{2} z + 3 y z^{2} + z^{3} - y^{3} - z^{3})^{2} - 18 y^{3} z^{3} = (3 y^{2} z + 3 y z^{2})^{2} - 18 y^{3} z^{3} = 9 y^{4} z^{2} + 18 y^{3} z^{3} + 9 y^{2} z^{4} - 18 y^{3} z^{3} = 9 y^{4} z^{2} + 9 y^{2} z^{4}

ГДЗ Алгебра 7 класс Дорофеев, Суворова, Бунимович