To find the simplest form of the expression [tex]\((2x - 3)(3x^2 + 2x - 1)\)[/tex], we need to expand it by applying the distributive property (also known as the FOIL method for binomials, but here more generally for polynomials).
We will multiply each term in the first polynomial by each term in the second polynomial:
[tex]\[
(2x - 3)(3x^2 + 2x - 1)
\][/tex]
First, distribute [tex]\(2x\)[/tex] to each term in [tex]\(3x^2 + 2x - 1\)[/tex]:
1. [tex]\(2x \cdot 3x^2 = 6x^3\)[/tex]
2. [tex]\(2x \cdot 2x = 4x^2\)[/tex]
3. [tex]\(2x \cdot (-1) = -2x\)[/tex]
Now distribute [tex]\(-3\)[/tex] to each term in [tex]\(3x^2 + 2x - 1\)[/tex]:
1. [tex]\(-3 \cdot 3x^2 = -9x^2\)[/tex]
2. [tex]\(-3 \cdot 2x = -6x\)[/tex]
3. [tex]\(-3 \cdot (-1) = 3\)[/tex]
Combine all these terms together:
[tex]\[
6x^3 + 4x^2 - 2x - 9x^2 - 6x + 3
\][/tex]
Next, combine like terms:
[tex]\[
6x^3 + (4x^2 - 9x^2) + (-2x - 6x) + 3
\][/tex]
[tex]\[
6x^3 - 5x^2 - 8x + 3
\][/tex]
Therefore, the simplest form of the expression [tex]\((2x - 3)(3x^2 + 2x - 1)\)[/tex] is:
[tex]\[
6x^3 - 5x^2 - 8x + 3
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{6x^3 - 5x^2 - 8x + 3}
\][/tex]
Hence, option B is correct.
