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].
