Question

Simplify:



left-parenthesis 2 x minus 3 right-parenthesis squared

Answer options with 4 options
A.
4 x squared minus 9

B.
4 x squared plus 9

C.
4 x squared minus 6 x minus 9

D.
4 x squared minus 12 x plus 9

Answer 1

To simplify the expression \((2x - 3)^2\), we can use the formula for squaring a binomial, which is:

\[
(a - b)^2 = a^2 - 2ab + b^2
\]

Here, let \(a = 2x\) and \(b = 3\). Applying the formula:

1. Calculate \(a^2\):
\[
(2x)^2 = 4x^2
\]

2. Calculate \(-2ab\):
\[
-2(2x)(3) = -12x
\]

3. Calculate \(b^2\):
\[
3^2 = 9
\]

Putting it all together, we get:
\[
(2x - 3)^2 = 4x^2 - 12x + 9
\]

Now, let's compare this with the answer options:

A. \(4x^2 - 9\)

B. \(4x^2 + 9\)

C. \(4x^2 - 6x - 9\)

D. \(4x^2 - 12x + 9\)

The correct answer is:

**D. \(4x^2 - 12x + 9\)**