College

What is the product?

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

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

B. [tex]14x^7-56x^8-126x^5+35x^4-140x^3-315x^2[/tex]

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

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

Answer :

To find the product of the expression [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex], follow these steps:

1. Multiply [tex]\(7x^2\)[/tex] with [tex]\((2x^3 + 5)\)[/tex]:

- Start with each term in the expression [tex]\( (2x^3 + 5) \)[/tex]:
- Multiply [tex]\(7x^2\)[/tex] by [tex]\(2x^3\)[/tex]: [tex]\(7x^2 \cdot 2x^3 = 14x^5\)[/tex]
- Multiply [tex]\(7x^2\)[/tex] by [tex]\(5\)[/tex]: [tex]\(7x^2 \cdot 5 = 35x^2\)[/tex]

- So, the result of the multiplication is: [tex]\(14x^5 + 35x^2\)[/tex].

2. Multiply the result by [tex]\((x^2 - 4x - 9)\)[/tex]:

- Distribute each term from [tex]\(14x^5 + 35x^2\)[/tex] across the terms in [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 all these terms:

- The expression from the multiplications is:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]

This is the final product of the expression [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex].

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