1. **State the problem:** Multiply the two polynomials $$(x^2 + 5x + 4)(x^2 + 2x - 1)$$. 2. **Use the distributive property:** Multiply each term in the first polynomial by each term in the second polynomial. 3. Multiply $x^2$ by each term: $$x^2 \times x^2 = x^4$$ $$x^2 \times 2x = 2x^3$$ $$x^2 \times (-1) = -x^2$$ 4. Multiply $5x$ by each term: $$5x \times x^2 = 5x^3$$ $$5x \times 2x = 10x^2$$ $$5x \times (-1) = -5x$$ 5. Multiply $4$ by each term: $$4 \times x^2 = 4x^2$$ $$4 \times 2x = 8x$$ $$4 \times (-1) = -4$$ 6. **Combine all terms:** $$x^4 + 2x^3 - x^2 + 5x^3 + 10x^2 - 5x + 4x^2 + 8x - 4$$ 7. **Group like terms:** - $x^4$ term: $$x^4$$ - $x^3$ terms: $$2x^3 + 5x^3 = 7x^3$$ - $x^2$ terms: $$-x^2 + 10x^2 + 4x^2 = 13x^2$$ - $x$ terms: $$-5x + 8x = 3x$$ - Constant term: $$-4$$ 8. **Final expanded polynomial:** $$x^4 + 7x^3 + 13x^2 + 3x - 4$$