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: \[ \boxed{-4x^2 + 20x - 25} \]

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