1. **State the problem:** We need to expand and simplify the expression $$y = (7x + 1)(x^3 - 2x - 9n)$$ where $x$ and $n$ are variables. 2. **Recall the distributive property:** To multiply two polynomials, multiply each term in the first polynomial by each term in the second polynomial. 3. **Multiply each term:** $$7x \cdot x^3 = 7x^4$$ $$7x \cdot (-2x) = -14x^2$$ $$7x \cdot (-9n) = -63xn$$ $$1 \cdot x^3 = x^3$$ $$1 \cdot (-2x) = -2x$$ $$1 \cdot (-9n) = -9n$$ 4. **Write the expanded expression:** $$y = 7x^4 - 14x^2 - 63xn + x^3 - 2x - 9n$$ 5. **Combine like terms:** There are no like terms to combine here, so this is the simplified form. **Final answer:** $$y = 7x^4 + x^3 - 14x^2 - 63xn - 2x - 9n$$