Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Multiply: [tex] (9x + 8)(3x^2 + x - 1) [/tex]

A. [tex] 27x^3 + 33x^2 + 17x + 8 [/tex]
B. [tex] 27x^3 + 33x^2 - x - 8 [/tex]
C. [tex] 27x^3 + 9x^2 - 8 [/tex]
D. [tex] 3x^2 + 10x + 7 [/tex]

To solve the multiplication of the expressions [tex]\((9x + 8)\)[/tex] and [tex]\((3x^2 + x - 1)\)[/tex], we can use the distributive property, also known as the FOIL method for binomials. However, since one expression is a binomial and the other is a trinomial, we'll distribute each term in the first expression across every term in the second expression. Let's break it down step-by-step:

1. Distribute [tex]\(9x\)[/tex]:

- Multiply [tex]\(9x\)[/tex] by [tex]\(3x^2\)[/tex]:
[tex]\[
9x \cdot 3x^2 = 27x^3
\][/tex]

- Multiply [tex]\(9x\)[/tex] by [tex]\(x\)[/tex]:
[tex]\[
9x \cdot x = 9x^2
\][/tex]

- Multiply [tex]\(9x\)[/tex] by [tex]\(-1\)[/tex]:
[tex]\[
9x \cdot -1 = -9x
\][/tex]

2. Distribute [tex]\(8\)[/tex]:

- Multiply [tex]\(8\)[/tex] by [tex]\(3x^2\)[/tex]:
[tex]\[
8 \cdot 3x^2 = 24x^2
\][/tex]

- Multiply [tex]\(8\)[/tex] by [tex]\(x\)[/tex]:
[tex]\[
8 \cdot x = 8x
\][/tex]

- Multiply [tex]\(8\)[/tex] by [tex]\(-1\)[/tex]:
[tex]\[
8 \cdot -1 = -8
\][/tex]

3. Combine like terms:

- The [tex]\(x^3\)[/tex] term is [tex]\(27x^3\)[/tex].

- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(9x^2 + 24x^2\)[/tex]:
[tex]\[
9x^2 + 24x^2 = 33x^2
\][/tex]

- Combine the [tex]\(x\)[/tex] terms: [tex]\(-9x + 8x\)[/tex]:
[tex]\[
-9x + 8x = -1x
\][/tex]

- The constant term is [tex]\(-8\)[/tex].

Putting it all together, the expanded polynomial is:

[tex]\[
27x^3 + 33x^2 - x - 8
\][/tex]

This is the result of multiplying the two expressions.