The expression given is $(x - 6)^2$. Let's expand this expression using the formula for squaring a binomial:

$(a - b)^2 = a^2 - 2ab + b^2$

Here, $a = x$ and $b = 6$, so:

$(x - 6)^2 = x^2 - 2(x)(6) + 6^2$ $= x^2 - 12x + 36$

Thus, the correct equivalent expression is:

$x^2 - 12x + 36$

Looking at the provided options, the third option $x^2 - 12x + 36$ is the correct answer.

Do you have any questions, or would you like further details?

Here are 5 related questions:

1. What is the general formula for expanding $(a - b)^2$?
2. How would you expand $(x + 5)^2$?
3. What is the difference between $(x - 6)^2$ and $(x + 6)^2$?
4. Can you factor $x^2 - 12x + 36$ back into its binomial form?
5. What happens if you expand $(2x - 6)^2$?

Tip: When squaring a binomial, remember to apply the formula $(a \pm b)^2 = a^2 \pm 2ab + b^2$ for quick expansion.