Question

Find the product of (4x3+2x2)(6x−9)
. Provide your answer in descending order of exponents.

(1 point)
(4x3+2x2)(6x−9)=

Answer 1

To find the product of \((4x^3 + 2x^2)(6x - 9)\), we can use the distributive property (also known as the FOIL method for binomials).

1. Distribute each term in the first polynomial by each term in the second polynomial:
\[
(4x^3)(6x) + (4x^3)(-9) + (2x^2)(6x) + (2x^2)(-9)
\]

2. Calculate each of these products:
- \(4x^3 \cdot 6x = 24x^4\)
- \(4x^3 \cdot -9 = -36x^3\)
- \(2x^2 \cdot 6x = 12x^3\)
- \(2x^2 \cdot -9 = -18x^2\)

3. Now combine these results:
\[
24x^4 + (-36x^3 + 12x^3) + (-18x^2)
\]

4. Combine like terms:
- For \(x^3\) terms: \(-36x^3 + 12x^3 = -24x^3\)

Thus, the combined result is:
\[
24x^4 - 24x^3 - 18x^2
\]

Putting this all together, we write the final answer in descending order:
\[
\boxed{24x^4 - 24x^3 - 18x^2}
\]