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\begin{tabular}{|c|c|c|}
[tex]$4x^3$[/tex] & [tex]$2x^2$[/tex] & \\
\hline [tex]$24x^4$[/tex] & [tex]$12x^3$[/tex] & [tex]$6x$[/tex] \\
\hline [tex]$-36x^3$[/tex] & [tex]$-18x^2$[/tex] & -9 \\
\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)

[tex]$\left(4x^3 + 2x^2\right)(6x - 9) = \square$[/tex]

Sagot :

GinnyAnsweridn
Let's find the product [tex]\((4x^3 + 2x^2)(6x - 9)\)[/tex] step by step.

First, distribute [tex]\(6x\)[/tex] to each term in the first polynomial:

[tex]\[6x \cdot 4x^3 = 24x^4\][/tex]

[tex]\[6x \cdot 2x^2 = 12x^3\][/tex]

Next, distribute [tex]\(-9\)[/tex] to each term in the first polynomial:

[tex]\[-9 \cdot 4x^3 = -36x^3\][/tex]

[tex]\[-9 \cdot 2x^2 = -18x^2\][/tex]

Now, combine all these products:

[tex]\[24x^4 + 12x^3 - 36x^3 - 18x^2\][/tex]

Combine like terms:

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

Simplify the expression inside the parentheses:

[tex]\[24x^4 + (-24x^3) - 18x^2\][/tex]

So, the final product is:

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

Thus, the product [tex]\((4x^3 + 2x^2)(6x - 9)\)[/tex] is [tex]\(\boxed{24x^4 - 24x^3 - 18x^2}\)[/tex].
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