Find the product of (4x3+2x2)(6x−9)

Question

(
4
𝑥
3
+
2
𝑥
2
)
(
6
𝑥
−
9
)
. Provide your answer in descending order of exponents.

(1 point)
(4x3+2x2)(6x−9)=
(
4
𝑥
3
+
2
𝑥
2
)
(
6
𝑥
−
9
)
=

Answer 1

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

1. Distribute \( 4x^3 \) to both terms in the second polynomial: \[ 4x^3 \cdot 6x = 24x^4 \] \[ 4x^3 \cdot (-9) = -36x^3 \]

2. Now distribute \( 2x^2 \) to both terms in the second polynomial: \[ 2x^2 \cdot 6x = 12x^3 \] \[ 2x^2 \cdot (-9) = -18x^2 \]

3. Now, combine all the products: \[ 24x^4 - 36x^3 + 12x^3 - 18x^2 \]

4. Combine like terms: \[ -36x^3 + 12x^3 = -24x^3 \]

So, the final expression in descending order of exponents is: \[ 24x^4 - 24x^3 - 18x^2 \]

Thus, the answer is: \[ \boxed{24x^4 - 24x^3 - 18x^2} \]