To solve this problem, we need to expand the expression $(x - 3)^2$ and see which option matches the result.

Step-by-Step Solution:

1. Use the formula for expanding a square of a binomial: $(a - b)^2 = a^2 - 2ab + b^2$ Here, $a = x$ and $b = 3$.

2. Apply the formula: $(x - 3)^2 = x^2 - 2 \cdot x \cdot 3 + 3^2$

3. Calculate each term:

   • $x^2$ remains as $x^2$.
   • $-2 \cdot x \cdot 3 = -6x$.
   • $3^2 = 9$.

4. Combine terms: $x^2 - 6x + 9$

Conclusion:

The expression equivalent to $(x - 3)^2$ is $x^2 - 6x + 9$, which corresponds to Option A.

Would you like further details or have any questions?

Here are five related questions to expand your understanding:

1. How would you expand $(x + 4)^2$?
2. What is the result of $(x - 5)^2$?
3. Can you find the expanded form of $(2x - 3)^2$?
4. How does the formula change for $(a + b)^2$?
5. How would you simplify $(2x + 1)^2$?

Tip: Remember that $(a - b)^2$ always results in $a^2 - 2ab + b^2$, so focus on applying this structure when expanding similar expressions.