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x^{2}-2x+1-\left(x-2\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.
x^{2}-2x+1-x+2
To find the opposite of x-2, find the opposite of each term.
x^{2}-3x+1+2
Combine -2x and -x to get -3x.
x^{2}-3x+3
Add 1 and 2 to get 3.
x^{2}-2x+1-\left(x-2\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.
x^{2}-2x+1-x+2
To find the opposite of x-2, find the opposite of each term.
x^{2}-3x+1+2
Combine -2x and -x to get -3x.
x^{2}-3x+3
Add 1 and 2 to get 3.