The structure is that the pattern is the difference of two squares.
Let a = 5x - 11 and b = 3x + 4 thus the expression to be factored can be represented as a2 - b2 which factor into
(a - b)(a + b). Replacing a with 5x - 11 and b with 3x + 4 we obtain [(5x - 11) - (3x +4)][(5x - 11) + (3x + 4)]
by simplifying we obtain [5x - 11 - 3x - 4][5x - 11 + 3x + 4] = [2x - 15][8x - 7]
Thus (5x - 11)2 - (3x + 4)2 = (2x - 15)(8x - 7)