The square of 5-√y^2-25 is:

1954 AMC 12 Problem 1

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The square of

5-\sqrt{y^2-25}

is:

y^2-5\sqrt{y^2-25}

-y^2

y^2

(5-y)^2

y^2-10\sqrt{y^2-25}

Use

(a-b)^2=a^2-2ab+b^2

The constant

25

cancels with the

-25

inside the squared radical

Expanding gives

\begin{aligned} &\left(5-\sqrt{y^2-25}\right)^2\\ &\quad=25-10\sqrt{y^2-25}\\ &\qquad{}+y^2-25\\ &\quad=y^2-10\sqrt{y^2-25}. \end{aligned}

Thus, the correct answer is E.