1. **State the problem:** Simplify the expression $$(3 \times 5 - 3)^2 + (3 - 3 \times 6^2)$$. 2. **Recall order of operations:** Perform multiplication and exponents before addition and subtraction. 3. **Calculate inside the first parentheses:** $$3 \times 5 = 15$$ $$15 - 3 = 12$$ 4. **Square the result:** $$12^2 = 144$$ 5. **Calculate inside the second parentheses:** $$6^2 = 36$$ $$3 \times 36 = 108$$ $$3 - 108 = -105$$ 6. **Add the two results:** $$144 + (-105) = 39$$ **Final answer:** $$39$$