1. **State the problem:** Multiply the two polynomials $ (2x^2+4) $ and $ (x^2-3x+1) $. 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:** - $2x^2 \cdot x^2 = 2x^4$ - $2x^2 \cdot (-3x) = -6x^3$ - $2x^2 \cdot 1 = 2x^2$ - $4 \cdot x^2 = 4x^2$ - $4 \cdot (-3x) = -12x$ - $4 \cdot 1 = 4$ 4. **Combine like terms:** - Combine $2x^2$ and $4x^2$ to get $6x^2$ 5. **Write the final expression:** $$2x^4 - 6x^3 + 6x^2 - 12x + 4$$ This is the product of the two polynomials.