To factorize the expression 9x^2 + 4x^2 + 16z^2 + 12xy - 16yz - 24xz, we can group the terms with common factors:
(9x^2 + 4x^2) + (16z^2 - 16yz) + (12xy - 24xz)
Factor out the common factors from each group:
9x^2 + 4x^2 = 13x^2
16z^2 - 16yz = 16z(z - y)
12xy - 24xz = 12x(y - 2z)
Putting it all together, we have:
9x^2 + 4x^2 + 16z^2 + 12xy - 16yz - 24xz = 13x^2 + 16z(z - y) + 12x(y - 2z)
Therefore, 9x^2 + 4x^2 + 16z^2 + 12xy - 16yz - 24xz can be factorized as (13x^2 + 16z(z - y) + 12x(y - 2z)).