Question

Simplify (x - y)^2 - 2(x - y) + 1

Answer 1

Answer:

(x-y-1)^2 or [(x-y)-1]^2

Step-by-step explanation:

We are given the expression:-

$\displaystyle \large{ {(x - y)}^{2} - 2(x - y) + 1 }$

Let A = (x-y)^2

$\displaystyle \large{ A^{2} - 2 A+ 1 }$

From:-

$\displaystyle \large{ {x}^{2} - 2x + 1 = {(x - 1)}^{2} }$

Thus:-

$\displaystyle \large{ {A}^{2} - 2A + 1 = {( A- 1)}^{2} }$

Rewrite A in (x-y)^2.

$\displaystyle \large{ {(x - y)}^{2} - 2(x - y) + 1 = {( (x - y) - 1)}^{2} }$