Questions: Perform the indicated operation and simplify.
[
-(2 x-5)^2
]
(-(2 x-5)^2=) (square) (Simplify your answer.)
Transcript text: Perform the indicated operation and simplify.
\[
-(2 x-5)^{2}
\]
$-(2 x-5)^{2}=$ $\square$ (Simplify your answer.)
Solution
Solution Steps
Step 1: Expand the Expression
We start with the expression \(-(2x - 5)^2\). To simplify it, we first expand the square of the binomial:
\[
(2x - 5)^2 = (2x)^2 - 2 \cdot (2x) \cdot 5 + 5^2 = 4x^2 - 20x + 25
\]
Step 2: Apply the Negative Sign
Next, we apply the negative sign to the expanded expression:
\[
-(4x^2 - 20x + 25) = -4x^2 + 20x - 25
\]
Final Answer
The simplified expression is:
\[
\boxed{-4x^2 + 20x - 25}
\]