1. **State the problem:** Factorise fully the expression $$8ax - 14bx + 4ay - 7by$$.
2. **Identify common factors:** Group terms to find common factors:
$$8ax - 14bx + 4ay - 7by = (8ax - 14bx) + (4ay - 7by)$$
3. **Factor each group:**
$$8ax - 14bx = 2x(4a - 7b)$$
$$4ay - 7by = y(4a - 7b)$$
4. **Factor out the common binomial:**
$$2x(4a - 7b) + y(4a - 7b) = (4a - 7b)(2x + y)$$
5. **Final answer:**
$$\boxed{(4a - 7b)(2x + y)}$$
This is the fully factorised form of the given expression.
Factorise Expression 272D9C
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