factor.\nu^{2}-10u + 25

Explanation:

Step1: Recall the formula for perfect - square trinomial

The formula for a perfect - square trinomial is (a^{2}-2ab + b^{2}=(a - b)^{2}).

Step2: Identify (a) and (b) in the given trinomial

For the trinomial (u^{2}-10u + 25), we have (a^{2}=u^{2}), so (a = u), and (b^{2}=25), so (b = 5). Also, (2ab=2\times u\times5 = 10u).

Step3: Apply the formula

Substitute (a = u) and (b = 5) into the formula (a^{2}-2ab + b^{2}=(a - b)^{2}). We get (u^{2}-10u + 25=(u - 5)^{2}).

Answer:

((u - 5)^{2})