Question

(4x3+2x2)(6x−9)

Answer 1

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

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

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 we combine all the terms:
\[
24x^4 + (-36x^3 + 12x^3) - 18x^2
\]

4. Combine like terms:
\[
24x^4 + (-36x^3 + 12x^3) = 24x^4 - 24x^3
\]
So, we have:
\[
24x^4 - 24x^3 - 18x^2
\]

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