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