What is the product?

[tex]\[ \left(7x^2\right)\left(2x^3+5\right)\left(x^2-4x-9\right) \][/tex]

A. [tex]$ 14x^5 - x^4 - 46x^3 = 58x^2 - 20x - 45 $[/tex]

B. [tex]$ 14x^6 - 56x^5 - 91x^4 - 140x^3 - 315x^2 $[/tex]

C. [tex]$ 14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2 $[/tex]

D. [tex]$ 14x^{12} - 182x^6 + 35x^4 - 455x^2 $[/tex]

To find the product of the expressions [tex]$(7x^2)(2x^3 + 5)(x^2 - 4x - 9)$[/tex], let's break it down step by step:

1. Identify and Multiply the First Two Terms:
- Start by multiplying [tex]$7x^2$[/tex] with the second term, [tex]$(2x^3 + 5)$[/tex].
- Distribute [tex]$7x^2$[/tex] across each term in [tex]$(2x^3 + 5)$[/tex]:
- [tex]$7x^2 \cdot 2x^3 = 14x^5$[/tex]
- [tex]$7x^2 \cdot 5 = 35x^2$[/tex]
- So, the product of the first two terms is [tex]$14x^5 + 35x^2$[/tex].

2. Multiply the Result with the Third Term:
- Now, take the expression [tex]$14x^5 + 35x^2$[/tex] and multiply it with [tex]$(x^2 - 4x - 9)$[/tex].
- Distribute each term in [tex]$14x^5 + 35x^2$[/tex] across [tex]$(x^2 - 4x - 9)$[/tex]:

For [tex]$14x^5$[/tex]:
- [tex]$14x^5 \cdot x^2 = 14x^7$[/tex]
- [tex]$14x^5 \cdot (-4x) = -56x^6$[/tex]
- [tex]$14x^5 \cdot (-9) = -126x^5$[/tex]

For [tex]$35x^2$[/tex]:
- [tex]$35x^2 \cdot x^2 = 35x^4$[/tex]
- [tex]$35x^2 \cdot (-4x) = -140x^3$[/tex]
- [tex]$35x^2 \cdot (-9) = -315x^2$[/tex]

3. Combine Like Terms:
- Now, combine all these terms:
- [tex]$14x^7$[/tex]
- [tex]$-56x^6$[/tex]
- [tex]$-126x^5$[/tex]
- [tex]$35x^4$[/tex]
- [tex]$-140x^3$[/tex]
- [tex]$-315x^2$[/tex]

4. Write the Final Expression:
- The result of combining and arranging these terms is:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]

This final expression is the product of the given terms.