Find the product of (4x3+2x2)(6x−9) . Provide your answer in descending order of exponents.

Question

(1 point)
(4x3+2x2)(6x−9)=

Answer 1

To find the product of the expressions $(4x^3+2x^2)(6x-9)$, we'll follow these steps:

1. 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:

$$\boxed{{\displaystyle 24x^4-24x^3-18x^2}}$$