[tex]\displaystyle\bf\\a^{2} - b^{2} +4a+4=(a^{2} +4a+4)-b^{2}= \\\\=(a^{2} +2\cdot a\cdot 2+2^{2} )-b^{2} =(a+2)^{2} -b^{2} =\\\\=(a+2-b)\cdot(a+2+b)[/tex]