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\left(1-x\right)\left(1+x\right)
Rewrite 1-x^{2} as 1^{2}-x^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
\left(-x+1\right)\left(x+1\right)
Reorder the terms.