(5 + a)(b - 6) - ab + 6a при a = 3 + 4\sqrt{7}, b = 7.

Решим предложенные алгебраические выражения: 1. $(5 + a)(b - 6) - ab + 6a$ Раскроем скобки: $5b - 30 + ab - 6a - ab + 6a = 5b - 30$. Подставим $b = 7$: $5 \cdot 7 - 30 = 35 - 30 = 5$. 2. $(x - 2)(x + 5) - (x + 3)(x - 4)$ Раскроем скобки: $(x^2 + 5x - 2x - 10) - (x^2 - 4x + 3x - 12) = x^2 + 3x - 10 - x^2 + x + 12 = 4x + 2$. Подставим $x = -4,5$: $4 \cdot (-4,5) + 2 = -18 + 2 = -16$. 3. $(5a - 2b) - (3b - 4a) = 5a - 2b - 3b + 4a = 9a - 5b$. 4. $(6c - b) - (2c + 3b) = 6c - b - 2c - 3b = 4c - 4b$. 5. $2x - (3x + y) + 6y = 2x - 3x - y + 6y = -x + 5y$. 6. $8x - (3x - 2y) - 7y = 8x - 3x + 2y - 7y = 5x - 5y$. 7. $0,5(a - 3b) - (3b + 0,5a) = 0,5a - 1,5b - 3b - 0,5a = -4,5b$. 9. $(5a^2 - 0,4b^2)(0,4b^2 + 5a^2) = (5a^2 - 0,4b^2)(5a^2 + 0,4b^2) = (5a^2)^2 - (0,4b^2)^2 = 25a^4 - 0,16b^4$. 10. $(2,5x - 0,3y)(2,5x + 0,3y) = (2,5x)^2 - (0,3y)^2 = 6,25x^2 - 0,09y^2$. 11. $a^2 - 64b^2 = a^2 - (8b)^2 = (a - 8b)(a + 8b)$. 12. $36 - x^2y^2 = 6^2 - (xy)^2 = (6 - xy)(6 + xy)$. 13. $(2p - m)^2 - (p + 2m)^2 = (4p^2 - 4pm + m^2) - (p^2 + 4pm + 4m^2) = 4p^2 - 4pm + m^2 - p^2 - 4pm - 4m^2 = 3p^2 - 8pm - 3m^2$. 14. $(3a - 2b)^2 - (4a + b)^2 = (9a^2 - 12ab + 4b^2) - (16a^2 + 8ab + b^2) = 9a^2 - 12ab + 4b^2 - 16a^2 - 8ab - b^2 = -7a^2 - 20ab + 3b^2$. 15. $25z^2 - (2t + 3z)^2 = (5z)^2 - (2t + 3z)^2 = (5z - (2t + 3z))(5z + (2t + 3z)) = (5z - 2t - 3z)(5z + 2t + 3z) = (2z - 2t)(8z + 2t)$.