1. **State the problem:** Factorise the expression $a(b-c)^2 - d(c-b)$. 2. **Rewrite the expression:** Notice that $c-b = -(b-c)$, so replace $d(c-b)$ with $-d(b-c)$. The expression becomes $$a(b-c)^2 - d(c-b) = a(b-c)^2 + d(b-c).$$ 3. **Factor out the common term:** Both terms contain $(b-c)$, so factor it out: $$= (b-c)(a(b-c) + d).$$ 4. **Final factorised form:** $$\boxed{(b-c)(a(b-c) + d)}.$$ This is the fully factorised form of the given expression.