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