The given expression to factor is:

$1 - (2x - 3)^2$

This is a difference of squares. The general formula for factoring a difference of squares is:

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

Here, we can rewrite the expression as:

$1^2 - (2x - 3)^2$

Now, using the difference of squares formula, we have:

$(1 - (2x - 3))(1 + (2x - 3))$

Simplify both factors:

$1 - (2x - 3) = 1 - 2x + 3 = 4 - 2x$ $1 + (2x - 3) = 1 + 2x - 3 = 2x - 2$

Thus, the factored form is:

$(4 - 2x)(2x - 2)$

Now, let’s simplify further. We can factor out common factors:

$(4 - 2x) = 2(2 - x)$ $(2x - 2) = 2(x - 1)$

So the final factored form is:

$2(2 - x) \cdot 2(x - 1) = 4(2 - x)(x - 1)$

The correct answer corresponds to option C: $4(2 - x)(x - 1)$.

Would you like more details or further clarification?

Here are 5 related questions:

1. How do you expand a difference of squares?
2. What is the difference of squares formula and when is it used?
3. How can we factor common terms in a polynomial?
4. What steps do you follow to fully factor an expression?
5. How can factoring help simplify algebraic expressions?

Tip: Always check for common factors first before applying other factoring techniques like difference of squares.