1. **State the problem:** Simplify the expression $6px + 10py + 18qx + 30qy$ by factoring common terms. 2. **Identify common factors:** Group terms with common variables: $$6px + 18qx + 10py + 30qy$$ 3. **Factor each group:** $$x(6p + 18q) + y(10p + 30q)$$ 4. **Factor out common factors inside parentheses:** $$x \cdot 6(p + 3q) + y \cdot 10(p + 3q)$$ 5. **Factor out the common binomial $(p + 3q)$:** $$ (p + 3q)(6x + 10y)$$ 6. **Factor out common factor 2 from $(6x + 10y)$:** $$ (p + 3q) \cdot 2(3x + 5y)$$ 7. **Final simplified form:** $$2(p + 3q)(3x + 5y)$$ This is the fully factored form of the original expression.