factor $d^{2}-10d + 25$

Explanation:

Step1: Check if it is a perfect - square trinomial

For a trinomial (a^{2}-2ab + b^{2}=(a - b)^{2}). In (d^{2}-10d + 25), (a = d), (2ab=10d), so (b = 5) (since (2\times d\times b=10d\Rightarrow b = 5)), and (b^{2}=25).

Step2: Apply the perfect - square formula

Since (d^{2}-10d + 25=d^{2}-2\times d\times5+5^{2}), by the formula (a^{2}-2ab + b^{2}=(a - b)^{2}), we have (d^{2}-10d + 25=(d - 5)^{2}=(d - 5)(d - 5))

Answer:

((d - 5)(d - 5))