Question

Find the product of (4x^3+2x^2)(6x−9) . Provide your answer in descending order of exponents. (1 point) (4x^3+2x^2)(6x−9

Answer 1

To find the product of \((4x^3 + 2x^2)(6x - 9)\), we will use the distributive property (also known as the FOIL method for binomials).

Let's distribute each term in the first polynomial \((4x^3 + 2x^2)\) to each term in the second polynomial \((6x - 9)\):

1. Multiply \(4x^3\) by \(6x\):
\[
4x^3 \cdot 6x = 24x^4
\]

2. Multiply \(4x^3\) by \(-9\):
\[
4x^3 \cdot (-9) = -36x^3
\]

3. Multiply \(2x^2\) by \(6x\):
\[
2x^2 \cdot 6x = 12x^3
\]

4. Multiply \(2x^2\) by \(-9\):
\[
2x^2 \cdot (-9) = -18x^2
\]

Now, we can combine all the terms we obtained:
\[
24x^4 - 36x^3 + 12x^3 - 18x^2
\]

Next, we combine the like terms for \(x^3\):
\[
-36x^3 + 12x^3 = -24x^3
\]

So, we have:
\[
24x^4 - 24x^3 - 18x^2
\]

Putting it all together, the final expression in descending order of exponents is:
\[
\boxed{24x^4 - 24x^3 - 18x^2}
\]