To factor the perfect square trinomial \(x^2 - 26xy + 169y^2\), we need to recognize that it is in the form of \((a - b)^2\), where \(a\) and \(b\) are terms that will give us the trinomial when squared.
1. Identify the square root of the first and last terms:
- The square root of \(x^2\) is \(x\).
- The square root of \(169y^2\) is \(13y\).
2. Determine the middle term by taking twice the product of the square roots:
- \(2 \times x \times 13y = 26xy\).
3. Rewrite the trinomial using the square roots:
- \((x - 13y)^2\).
Therefore, the factored form of the perfect square trinomial \(x^2 - 26xy + 169y^2\) is \((x - 13y)^2\).
