1. **State the problem:** Find the product and simplify the expression $$-4t^{2}(4t^{2} - t + 1)$$. 2. **Formula and rules:** To multiply a monomial by a polynomial, multiply the monomial by each term inside the parentheses. 3. **Multiply each term:** $$-4t^{2} \times 4t^{2} = -16t^{4}$$ $$-4t^{2} \times (-t) = +4t^{3}$$ $$-4t^{2} \times 1 = -4t^{2}$$ 4. **Combine all terms:** $$-16t^{4} + 4t^{3} - 4t^{2}$$ 5. **Final answer:** The simplified product is $$\boxed{-16t^{4} + 4t^{3} - 4t^{2}}$$.