Find the product of (4𝑥^3+2^2) (6𝑥 - 9 ). Provide your answer in descending order of exponents.

Answer 1

To find the product of the two expressions \( (4x^3 + 2^2)(6x - 9) \), we first simplify the expression inside the first parentheses:

\[ 2^2 = 4 \]

So we have:

\[ (4x^3 + 4)(6x - 9) \]

Next, we can distribute each term in the first parentheses to each term in the second parentheses.

1. Distributing \( 4x^3 \):

\[ 4x^3 \cdot 6x = 24x^4 \] \[ 4x^3 \cdot (-9) = -36x^3 \]

2. Distributing \( 4 \):

\[ 4 \cdot 6x = 24x \] \[ 4 \cdot (-9) = -36 \]

Now we combine all these results:

\[ 24x^4 - 36x^3 + 24x - 36 \]

The final expression written in descending order of exponents is:

\[ \boxed{24x^4 - 36x^3 + 24x - 36} \]