To determine which expression is equal to $(x-3)(2x^2 - x + 3)$, let’s expand the expression step by step:

Step 1: Distribute $x$ to $(2x^2 - x + 3)$

$x \cdot (2x^2 - x + 3) = 2x^3 - x^2 + 3x$

Step 2: Distribute $-3$ to $(2x^2 - x + 3)$

$-3 \cdot (2x^2 - x + 3) = -6x^2 + 3x - 9$

Step 3: Combine both results

Now, add the terms together: $(2x^3 - x^2 + 3x) + (-6x^2 + 3x - 9)$

Combine like terms:

• $2x^3$ (no other $x^3$ term),
• $-x^2 - 6x^2 = -7x^2$,
• $3x + 3x = 6x$,
• Constant term: $-9$.

Final Expression:

$2x^3 - 7x^2 + 6x - 9$

Answer:

The correct option is: $\boxed{2x^3 - 7x^2 + 6x - 9}$

Do you need further clarification on any steps?

Here are 5 related questions to explore further:

1. How can we expand and simplify polynomial products like $(x-2)(3x^2 + x - 4)$?
2. How do you use the distributive property for polynomials?
3. What are the steps for factoring polynomials given expanded forms?
4. How do you verify polynomial identities using substitution?
5. What methods exist to multiply binomials quickly (like FOIL)?

Tip: Always combine like terms carefully when distributing polynomials!