141. Упростите выражение: 1) (x - 2)(x² + 2x + 4) + (4 - x)(x² + 4x + 16); 2) (x + 3)(x² - 3x + 9) - x(x - 4)(x + 4); 3) y(y + 3)(y - 3) - (y - 5)(y² + 5y + 25); 4) (x² + 1)(x⁴ + 1)(x⁸ + 1)(x¹⁶ + 1)(x³² + 1)(x⁶⁴ - x³² + 1).

Используем формулы суммы и разности кубов: 1) $(x - 2)(x^2 + 2x + 4) + (4 - x)(x^2 + 4x + 16) = (x^3 - 8) + (64 - x^3) = 56$ 2) $(x + 3)(x^2 - 3x + 9) - x(x - 4)(x + 4) = (x^3 + 27) - x(x^2 - 16) = x^3 + 27 - x^3 + 16x = 16x + 27$ 3) $y(y + 3)(y - 3) - (y - 5)(y^2 + 5y + 25) = y(y^2 - 9) - (y^3 - 125) = y^3 - 9y - y^3 + 125 = 125 - 9y$ 4) $(x² + 1)(x⁴ + 1)(x⁸ + 1)(x¹⁶ + 1)(x³² + 1)(x⁶⁴ - x³² + 1) = (x^2+1)(x^4+1)(x^8+1)(x^{16}+1)(x^{64}-x^{32}+x^{32}+1)(x^{64}+1) = (x^2+1)(x^4+1)(x^8+1)(x^{16}+1)(x^{64}+1) = \frac{(x^2-1)}{(x^2-1)}(x^2+1)(x^4+1)(x^8+1)(x^{16}+1)(x^{64}+1)= \frac{(x^4-1)}{(x^2-1)}(x^4+1)(x^8+1)(x^{16}+1)(x^{64}+1)= \frac{(x^8-1)}{(x^2-1)}(x^8+1)(x^{16}+1)(x^{64}+1) = \frac{(x^{16}-1)}{(x^2-1)}(x^{16}+1)(x^{64}+1) = \frac{(x^{32}-1)}{(x^2-1)}(x^{64}+1)= \frac{(x^{64}-1)}{(x^2-1)}(x^{64}+1) = \frac{x^{128} - 1}{x^2 - 1}$