Polynomial Product E83233

1. **State the problem:** We need to find the product of the two polynomials $6x^5 - 2x^3$ and $x^4 - 3x$. 2. **Formula and rules:** To multiply two polynomials, use the distributive property (also called FOIL for binomials), multiplying each term in the first polynomial by each term in the second polynomial. 3. **Multiply each term:** - Multiply $6x^5$ by $x^4$ to get $6x^{5+4} = 6x^9$. - Multiply $6x^5$ by $-3x$ to get $-18x^{5+1} = -18x^6$. - Multiply $-2x^3$ by $x^4$ to get $-2x^{3+4} = -2x^7$. - Multiply $-2x^3$ by $-3x$ to get $6x^{3+1} = 6x^4$. 4. **Write the expanded expression:** $$6x^9 - 18x^6 - 2x^7 + 6x^4$$ 5. **Combine like terms:** Arrange terms in descending order of exponents: $$6x^9 - 2x^7 - 18x^6 + 6x^4$$ 6. **Final answer:** $$6x^9 - 2x^7 - 18x^6 + 6x^4$$