1. Stating the problem: We need to factorize the equation $$4(u - y)^3 = (x - y)$$. 2. Rewrite the equation: The equation is already simplified as $$4(u - y)^3 = x - y$$. 3. To factorize, observe that the right side is a linear expression and the left side is a cubic expression in terms of $(u - y)$. 4. We can rewrite the equation as $$4(u - y)^3 - (x - y) = 0$$. 5. This is a difference of terms, but since the terms are not like powers or simple polynomials, direct factorization is limited. 6. However, we can express the equation as: $$4(u - y)^3 - (x - y) = 0$$ which can be seen as a polynomial in terms of $(u - y)$ and $(x - y)$. 7. If we consider $a = u - y$ and $b = x - y$, the equation becomes: $$4a^3 - b = 0$$ 8. This can be rearranged as: $$4a^3 = b$$ 9. Since $a$ and $b$ are expressions involving $u, x, y$, the factorization in terms of these variables is limited to this form. Final answer: The equation is already factored as $$4(u - y)^3 = (x - y)$$ or equivalently $$4(u - y)^3 - (x - y) = 0$$.