Let's find the product of the two given expressions, [tex]\((4x^3 + 2x^2)(6x - 9)\)[/tex], step by step.
First, we will distribute each term in the second expression, [tex]\(6x - 9\)[/tex], to each term in the first expression, [tex]\(4x^3 + 2x^2\)[/tex].
1. Distribute [tex]\(6x\)[/tex]:
[tex]\[
6x \cdot 4x^3 = 24x^4
\][/tex]
[tex]\[
6x \cdot 2x^2 = 12x^3
\][/tex]
2. Distribute [tex]\(-9\)[/tex]:
[tex]\[
-9 \cdot 4x^3 = -36x^3
\][/tex]
[tex]\[
-9 \cdot 2x^2 = -18x^2
\][/tex]
Now, we combine all these terms:
[tex]\[
24x^4 + 12x^3 - 36x^3 - 18x^2
\][/tex]
Next, we combine like terms:
[tex]\[
12x^3 - 36x^3 = -24x^3
\][/tex]
Therefore, the final expression is:
[tex]\[
24x^4 - 24x^3 - 18x^2
\][/tex]
So, the product of [tex]\((4x^3 + 2x^2)(6x - 9)\)[/tex] in descending order of exponents is:
[tex]\[
24x^4 - 24x^3 - 18x^2
\][/tex]
