What is the product?

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

Sure! To find the product of the given expression [tex]$(7x^2)(2x^3 + 5)(x^2 - 4x - 9)$[/tex], we'll follow these steps:

1. Distribute [tex]$7x^2$[/tex] into the second polynomial [tex]$(2x^3 + 5)$[/tex]:

[tex]\[
7x^2 \times (2x^3 + 5) = 7x^2 \times 2x^3 + 7x^2 \times 5
\][/tex]

Calculate:
- [tex]$7x^2 \times 2x^3 = 14x^5$[/tex]
- [tex]$7x^2 \times 5 = 35x^2$[/tex]

So, after this step, we have the expression:
[tex]\[
14x^5 + 35x^2
\][/tex]

2. Multiply the result from the previous step by the third polynomial [tex]$(x^2 - 4x - 9)$[/tex]:

[tex]$(14x^5 + 35x^2) \times (x^2 - 4x - 9)$[/tex]

Distribute each term of the first polynomial over each term of the second polynomial:

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

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

3. Combine all the terms:

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

So, the final result of the product is:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]

This is the expanded form of the product of the given expression.

What is the product?[tex]\[(7x^2)(2x^3 + 5)(x^2 - 4x - 9)\][/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]

Answer :

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