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\left(k-2m\right)\left(k+2m\right)
Rewrite -4m^{2}+k^{2} as k^{2}-\left(2m\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(-2m+k\right)\left(2m+k\right)
Reorder the terms.