Answer:
by pattern matching
Explanation:
Jaime matched the terms of the expression to the terms of the expansion of the square of a binomial.
(a-b)^2 = a^2 -2ab +b^2
By recognizing that x^4 is a square, and that 36y^2 is a square, Jaime could assign a=x^2 and b=6y and then test to see if 2ab matches the middle term.
2ab = 2(x^2)(6y) = 12x^2y . . . . matches the middle term
This tells Jaime that his pattern recognition was right on, and that the factoring is ...
(x^2 -6y)^2