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 the expressions \((4x^3 + 2x^2)(6x - 9)\), we'll follow these steps:

1. Distribute each term in the first polynomial to each term in the second polynomial.

Let's distribute \(4x^3\) and \(2x^2\):

\[
(4x^3)(6x) + (4x^3)(-9) + (2x^2)(6x) + (2x^2)(-9)
\]

Now, calculating each of these products:

- \(4x^3 \cdot 6x = 24x^4\)
- \(4x^3 \cdot -9 = -36x^3\)
- \(2x^2 \cdot 6x = 12x^3\)
- \(2x^2 \cdot -9 = -18x^2\)

Now combine these results:

\[
24x^4 + (-36x^3 + 12x^3) + (-18x^2)
\]

Combine the like terms for \(x^3\):

\[
-36x^3 + 12x^3 = -24x^3
\]

So, we can rewrite the expression as:

\[
24x^4 - 24x^3 - 18x^2
\]

Putting it all together, the final product in descending order of exponents is:

\[
\boxed{24x^4 - 24x^3 - 18x^2}
\]