Упростите выражение:
1)

(x + 1) (x^{2} - x + 1) + (2 - x) (4 + 2 x + x^{2})

;
2)

(x - 4) (x^{2} + 4 x + 16) - x (x - 5) (x + 5)

;
3)

a (a - 3)^{2} - (a + 3) (a^{2} - 3 a + 9)

;
4)

(a - 1) (a + 1) (a^{2} - a + 1) (a^{2} + a + 1) (a^{6} + 1) (a^{12} + 1)

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Алгебре 7 класс Мерзляк. Номер №685

(x + 1) (x^{2} - x + 1) + (2 - x) (4 + 2 x + x^{2}) = x^{3} + 1 + 2^{3} - x 3 = 1 + 8 = 9

(x - 4) (x^{2} + 4 x + 16) - x (x - 5) (x + 5) = x^{3} - 4^{3} - x (x^{2} - 25) = x^{3} - 64 - x^{3} + 25 x = 25 x - 64

a (a - 3)^{2} - (a + 3) (a^{2} - 3 a + 9) = a (a^{2} - 6 a + 9) - (a^{3} + 3^{3}) = a^{3} - 6 a^{2} + 9 a - a^{3} - 27 = - 6 a^{2} + 9 a - 27

(a - 1) (a + 1) (a^{2} - a + 1) (a^{2} + a + 1) (a^{6} + 1) (a^{12} + 1) = (a - 1) (a^{2} + a + 1) (a + 1) (a^{2} - a + 1) (a^{6} + 1) (a^{12} + 1) = (a^{3} - 1) (a^{3} + 1) (a^{6} + 1) (a^{12} + 1) = (a^{6} - 1) (a^{6} + 1) (a^{12} + 1) = (a^{12} - 1) (a^{12} + 1) = a^{24} - 1

ГДЗ Алгебра 7 класс Мерзляк, Полонский, Якир