Final answer:
To factorize the expression x^2 - 10x + 24 + 6y - 9y^2, we can group the terms and factorize each group separately.
Step-by-step explanation:
To factorize the expression x^2 - 10x + 24 + 6y - 9y^2, we need to identify common factors among the terms. In this case, we can group the terms as follows:
(x^2 - 10x + 24) + (6y - 9y^2)
The first group can be factored as a perfect square trinomial: (x - 4)(x - 6). The second group can be factored by taking out the common factor of y: 3y(2 - 3y).
So, the complete factorization is: (x - 4)(x - 6) + 3y(2 - 3y).