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]
