765. Разложите на множители:

Для решения всех примеров воспользуемся формулой разности квадратов: $a^2 - b^2 = (a - b)(a + b)$. а) $(x + y)^2 - (x - y)^2 = ((x + y) - (x - y))((x + y) + (x - y)) = (x + y - x + y)(x + y + x - y) = 2y \cdot 2x = 4xy$ б) $(2m - n)^2 - (m + 2n)^2 = ((2m - n) - (m + 2n))((2m - n) + (m + 2n)) = (2m - n - m - 2n)(2m - n + m + 2n) = (m - 3n)(3m + n)$ в) $(3n + 2p)^2 - (5p - 2n)^2 = ((3n + 2p) - (5p - 2n))((3n + 2p) + (5p - 2n)) = (3n + 2p - 5p + 2n)(3n + 2p + 5p - 2n) = (5n - 3p)(n + 7p)$ г) $4(3x - 2y)^2 - 9(4x + 3y)^2 = [2(3x - 2y)]^2 - [3(4x + 3y)]^2 = (6x - 4y)^2 - (12x + 9y)^2 = ((6x - 4y) - (12x + 9y))((6x - 4y) + (12x + 9y)) = (6x - 4y - 12x - 9y)(6x - 4y + 12x + 9y) = (-6x - 13y)(18x + 5y) = -(6x + 13y)(18x + 5y)$ д) $100(6a + 3b)^2 - 81(3a + 2b)^2 = [10(6a + 3b)]^2 - [9(3a + 2b)]^2 = (60a + 30b)^2 - (27a + 18b)^2 = ((60a + 30b) - (27a + 18b))((60a + 30b) + (27a + 18b)) = (60a + 30b - 27a - 18b)(60a + 30b + 27a + 18b) = (33a + 12b)(87a + 48b) = 3(11a + 4b) \cdot 3(29a + 16b) = 9(11a + 4b)(29a + 16b)$ е) $49(5x^2 + 8)^2 - 36(4x^2 - 1)^2 = [7(5x^2 + 8)]^2 - [6(4x^2 - 1)]^2 = (35x^2 + 56)^2 - (24x^2 - 6)^2 = ((35x^2 + 56) - (24x^2 - 6))((35x^2 + 56) + (24x^2 - 6)) = (35x^2 + 56 - 24x^2 + 6)(35x^2 + 56 + 24x^2 - 6) = (11x^2 + 62)(59x^2 + 50)$