Use the table to answer the question.

\begin{tabular}{|c|c|}
\hline [tex]$4x^3$[/tex] & [tex]$2x^2$[/tex] \\
\hline [tex]$24x^4$[/tex] & [tex]$12x^3$[/tex] \\
\hline [tex]$-36x^3$[/tex] & [tex]$-18x^2$[/tex] \\
\hline
\end{tabular}

Find the product of [tex]$\left(4x^3 + 2x^2\right)(6x - 9)$[/tex]. Provide your answer in descending order of exponents. (1 point)



Answer :

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]