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x^{2}+2x+1-\left(x+1\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-1
To find the opposite of x+1, find the opposite of each term.
x^{2}+x+1-1
Combine 2x and -x to get x.
x^{2}+x
Subtract 1 from 1 to get 0.
x^{2}+2x+1-\left(x+1\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-1
To find the opposite of x+1, find the opposite of each term.
x^{2}+x+1-1
Combine 2x and -x to get x.
x^{2}+x
Subtract 1 from 1 to get 0.