Factor the following binomial. $$ 121 x^{2}-25 $$ $$ ([?] x+\square)(\square x-\square) $$

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UpStudy AI · Accepted Answer

To factor the binomial $$ 121x^{2} - 25 $$, we can recognize it as a **difference of squares**.

Here's how it's done:

1. **Identify the squares:**
   - $$ 121x^{2} = (11x)^2 $$
   - $$ 25 = 5^2 $$

2. **Apply the difference of squares formula:**
   $$
   a^2 - b^2 = (a + b)(a - b)
   $$
   Substituting $$ a = 11x $$ and $$ b = 5 $$:
   $$
   (11x + 5)(11x - 5)
   $$

So, the factored form of $$ 121x^{2} - 25 $$ is:

$$
(11x + 5)(11x - 5)
$$

**Answer:** 
$$
(11x + 5)(11x - 5)
$$
$$ (11x + 5)(11x - 5) $$

Factor the following binomial.

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