Answer:
(x + 2y)(x + 2)(x - 2).
Explanation:
The expression x^(3) + 2x^(2)y - 4x - 8y can be factorized by grouping:
x^(3) + 2x^(2)y - 4x - 8y
= x^(2)(x + 2y) - 4(x + 2y)
= (x + 2y)(x^(2) - 4)
= (x + 2y)(x + 2)(x - 2)
Therefore, the expression can be factorized as (x + 2y)(x + 2)(x - 2).