Answer :

To find the product of the expression [tex]\((x-3)(2x^2 - 5x + 1)\)[/tex], we'll expand it step by step.

1. Distribute [tex]\(x\)[/tex] from the first term:

[tex]\(x \cdot (2x^2 - 5x + 1) = x \cdot 2x^2 - x \cdot 5x + x \cdot 1\)[/tex]

This results in:
[tex]\[ 2x^3 - 5x^2 + x \][/tex]

2. Distribute [tex]\(-3\)[/tex] from the second term:

[tex]\(-3 \cdot (2x^2 - 5x + 1) = -3 \cdot 2x^2 - (-3) \cdot 5x + (-3) \cdot 1\)[/tex]

This results in:
[tex]\[ -6x^2 + 15x - 3 \][/tex]

3. Combine all terms:

Now we combine the results from steps 1 and 2:
[tex]\[ 2x^3 - 5x^2 + x - 6x^2 + 15x - 3 \][/tex]

4. Combine like terms:

Collecting the terms with [tex]\(x^2\)[/tex] and [tex]\(x\)[/tex], we get:
[tex]\[ 2x^3 + (-5x^2 - 6x^2) + (x + 15x) - 3 = 2x^3 - 11x^2 + 16x - 3 \][/tex]

So, the expanded product of the expression [tex]\((x-3)(2x^2 - 5x + 1)\)[/tex] is:
[tex]\[ 2x^3 - 11x^2 + 16x - 3 \][/tex]