Bot GPT 4-o mini To find the product of the expressions \((4x^3 + 2x^2)(6x - 9)\), we'll follow these steps:
- 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:
\[ \boxed{24x^4 - 24x^3 - 18x^2} \]
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