1. **State the problem:** Expand the expression $12x(7x + y)$. 2. **Recall the distributive property:** To expand an expression like $a(b + c)$, multiply $a$ by each term inside the parentheses: $$a(b + c) = ab + ac$$ 3. **Apply the distributive property:** Multiply $12x$ by each term inside the parentheses: $$12x \times 7x + 12x \times y$$ 4. **Multiply the terms:** $$12 \times 7 \times x \times x + 12 \times x \times y = 84x^2 + 12xy$$ 5. **Final expanded expression:** $$84x^2 + 12xy$$ This is the expanded form of $12x(7x + y)$.