\[{x}^{2}-10x-{y}^{2}+25\]
1
Rewrite it in the form a2−2ab+b2{a}^{2}-2ab+{b}^{2}, where a=xa=x and b=5b=5.
x2−2(x)(5)+52−y2{x}^{2}-2(x)(5)+{5}^{2}-{y}^{2}

2
Use Square of Difference: (a−b)2=a2−2ab+b2{(a-b)}^{2}={a}^{2}-2ab+{b}^{2}.
(x−5)2−y2{(x-5)}^{2}-{y}^{2}

3
Use Difference of Squares: a2−b2=(a+b)(a−b){a}^{2}-{b}^{2}=(a+b)(a-b).
(x−5+y)(x−5−y)(x-5+y)(x-5-y)

Done
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