Упростите:

Решение:

1. \( (x - y)(x + y)(x^2 + y^2) = (x^2 - y^2)(x^2 + y^2) = (x^2)^2 - (y^2)^2 = x^4 - y^4 \)
2. \( (2a + b)(4a^2 + b^2)(2a - b) = (2a + b)(2a - b)(4a^2 + b^2) = ((2a)^2 - b^2)(4a^2 + b^2) = (4a^2 - b^2)(4a^2 + b^2) = (4a^2)^2 - (b^2)^2 = 16a^4 - b^4 \)
3. \( (c^3 + b)(c^3 - b)(c^6 + b^2) = ((c^3)^2 - b^2)(c^6 + b^2) = (c^6 - b^2)(c^6 + b^2) = (c^6)^2 - (b^2)^2 = c^{12} - b^4 \)
4. \( (3m - 2)(3m + 2) + 4 = (3m)^2 - 2^2 + 4 = 9m^2 - 4 + 4 = 9m^2 \)
5. \( 25n^2 - (7 + 5n)(7 - 5n) = 25n^2 - (7^2 - (5n)^2) = 25n^2 - (49 - 25n^2) = 25n^2 - 49 + 25n^2 = 50n^2 - 49 \)
6. \( 6x^2 - (x - 0.5)(x + 0.5) = 6x^2 - (x^2 - (0.5)^2) = 6x^2 - (x^2 - 0.25) = 6x^2 - x^2 + 0.25 = 5x^2 + 0.25 \)