Answered

Simplify:

[tex]\[
(2x - 3)^2
\][/tex]

A. [tex]\(4x^2 - 9\)[/tex]

B. [tex]\(4x^2 + 9\)[/tex]

C. [tex]\(4x^2 - 6x - 9\)[/tex]

D. [tex]\(4x^2 - 12x + 9\)[/tex]



Answer :

GinnyAnswer
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]

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