Answer:
(x-y-1)^2 or [(x-y)-1]^2
Step-by-step explanation:
We are given the expression:-
[tex] \displaystyle \large{ {(x - y)}^{2} - 2(x - y) + 1 }[/tex]
Let A = (x-y)^2
[tex] \displaystyle \large{ A^{2} - 2 A+ 1 }[/tex]
From:-
[tex] \displaystyle \large{ {x}^{2} - 2x + 1 = {(x - 1)}^{2} }[/tex]
Thus:-
[tex] \displaystyle \large{ {A}^{2} - 2A + 1 = {( A- 1)}^{2} }[/tex]
Rewrite A in (x-y)^2.
[tex] \displaystyle \large{ {(x - y)}^{2} - 2(x - y) + 1 = {( (x - y) - 1)}^{2} }[/tex]
