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2\left(x^{2}+y^{2}-1+2xy\right)
Factor out 2.
\left(x+y-1\right)\left(x+y+1\right)
Consider x^{2}+y^{2}-1+2xy. Rewrite x^{2}+y^{2}-1+2xy as \left(x+y\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
2\left(x+y-1\right)\left(x+y+1\right)
Rewrite the complete factored expression.