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\left(1-4x\right)\left(1+4x\right)
Rewrite 1-16x^{2} as 1^{2}-\left(4x\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
\left(-4x+1\right)\left(4x+1\right)
Reorder the terms.