To simplify the expression [tex]\((2x - 3)^2\)[/tex], follow these steps:
1. Understand the Square:
[tex]\((a - b)^2 = a^2 - 2ab + b^2\)[/tex]
2. Identify [tex]\(a\)[/tex] and [tex]\(b\)[/tex] in [tex]\((2x - 3)^2\)[/tex]:
Here, [tex]\(a = 2x\)[/tex] and [tex]\(b = 3\)[/tex].
3. Apply the formula:
[tex]\[
(2x - 3)^2 = (2x)^2 - 2 \cdot (2x) \cdot 3 + 3^2
\][/tex]
4. Calculate each term:
- [tex]\((2x)^2 = 4x^2\)[/tex]
- [tex]\(-2 \cdot (2x) \cdot 3 = -12x\)[/tex]
- [tex]\(3^2 = 9\)[/tex]
5. Combine the terms:
[tex]\[
4x^2 - 12x + 9
\][/tex]
Thus, the simplified form of [tex]\((2x - 3)^2\)[/tex] is:
[tex]\[
4x^2 - 12x + 9
\][/tex]
Therefore, the correct answer is:
D. [tex]\(4x^2 - 12x + 9\)[/tex]
