Упростите выражение:
1) $(x + 1)(x^2 - x + 1) + (2 - x)(4 + 2x + x^2)$;
2) $(x - 4)(x^2 + 4x + 16) - x(x - 5)(x + 5)$;
3) $a(a - 3)^2 - (a + 3)(a^2 - 3a + 9)$;
4) $(a - 1)(a + 1)(a^2 - a + 1)(a^2 + a + 1)(a^6 + 1)(a^{12} + 1)$.
$(x + 1)(x^2 - x + 1) + (2 - x)(4 + 2x + x^2) = x^3 + 1 + 2^3 - x3 = 1 + 8 = 9$
$(x - 4)(x^2 + 4x + 16) - x(x - 5)(x + 5) = x^3 - 4^3 - x(x^2 - 25) = x^3 - 64 - x^3 + 25x = 25x - 64$
$a(a - 3)^2 - (a + 3)(a^2 - 3a + 9) = a(a^2 - 6a + 9) - (a^3 + 3^3) = a^3 - 6a^2 + 9a - a^3 - 27 = -6a^2 + 9a - 27$
$(a - 1)(a + 1)(a^2 - a + 1)(a^2 + a + 1)(a^6 + 1)(a^{12} + 1) = (a - 1)(a^2 + a + 1)(a + 1)(a^2 - a + 1)(a^6 + 1)(a^{12} + 1) = (a^3 - 1)(a^3 + 1)(a^6 + 1)(a^{12} + 1) = (a^6 - 1)(a^6 + 1)(a^{12} + 1) = (a^{12} - 1)(a^{12} + 1) = a^{24} - 1$
Пожауйста, оцените решение
