5. Which of the following is equivalent to $$ x^{2}-25 $$ ? A. $$ x(x-25) $$ B. $$ (x-5)^{2} $$ C. $$ (x+5)(x-5) $$ D. $$ (x-25)^{2} $$ E. $$ \frac{(x+y)}{(x-y)} $$

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UpStudy AI · Accepted Answer

To determine which of the options is equivalent to $$ x^{2}-25 $$, we can recognize that $$ x^{2}-25 $$ is a difference of squares. The difference of squares can be factored using the formula:

$$
a^{2} - b^{2} = (a - b)(a + b)
$$

In this case, we can identify $$ a = x $$ and $$ b = 5 $$. Therefore, we can factor $$ x^{2}-25 $$ as follows:

$$
x^{2} - 25 = (x - 5)(x + 5)
$$

Now, let's evaluate the options provided:

A. $$ x(x-25) $$ - This does not match our factorization.

B. $$ (x-5)^{2} $$ - This is not equivalent to our factorization.

C. $$ (x+5)(x-5) $$ - This matches our factorization.

D. $$ (x-25)^{2} $$ - This does not match our factorization.

E. $$ \frac{(x+y)}{(x-y)} $$ - This is not relevant to our factorization.

Thus, the correct answer is:

**C. $$ (x+5)(x-5) $$**.
The correct answer is $$ (x+5)(x-5) $$, which is option C.

5. Which of the following is equivalent to \( x^{2}-25 \) ? A. \( x(x-25) \) B. \( (x-5)^{2} \) C. \( (x+5)(x-5) \) D. \( (x-25)^{2} \) E. \( \frac{(x+y)}{(x-y)} \)

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