1. **State the problem:** Multiply the two polynomials $$(x^2 + 2x - 1)(x^2 - x - 4)$$. 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:** - $x^2 \cdot x^2 = x^4$ - $x^2 \cdot (-x) = -x^3$ - $x^2 \cdot (-4) = -4x^2$ - $2x \cdot x^2 = 2x^3$ - $2x \cdot (-x) = -2x^2$ - $2x \cdot (-4) = -8x$ - $-1 \cdot x^2 = -x^2$ - $-1 \cdot (-x) = +x$ - $-1 \cdot (-4) = +4$ 4. **Combine all terms:** $$x^4 - x^3 - 4x^2 + 2x^3 - 2x^2 - 8x - x^2 + x + 4$$ 5. **Group like terms:** - $x^4$ - $(-x^3 + 2x^3) = x^3$ - $(-4x^2 - 2x^2 - x^2) = -7x^2$ - $(-8x + x) = -7x$ - $4$ 6. **Write the simplified polynomial:** $$x^4 + x^3 - 7x^2 - 7x + 4$$ **Final answer:** $$x^4 + x^3 - 7x^2 - 7x + 4$$