A) \[4({{a}^{2}}{{b}^{2}}-4{{c}^{2}})(ab-2c)(ab+2c)\]
B) \[({{a}^{2}}{{b}^{2}}-4{{c}^{2}})(ab+2{{c}^{2}})\]
C) \[({{a}^{2}}{{b}^{2}}+4{{c}^{2}})(ab+2c)(ab-2c)\]
D) \[({{a}^{2}}{{b}^{2}}-4{{c}^{2}})(ab+2c)(ab-4c)\]
Correct Answer: C
Solution :
\[({{a}^{4}}{{b}^{4}}-16{{c}^{4}})=[{{({{a}^{2}}{{b}^{2}})}^{2}}-{{(4{{c}^{2}})}^{2}}]\] \[=({{a}^{2}}{{b}^{2}}+4{{c}^{2}})[({{a}^{2}}{{b}^{2}}-4{{c}^{2}}]\] \[=({{a}^{2}}{{b}^{2}}+4{{c}^{2}})[{{(ab)}^{2}}-{{(2c)}^{2}}]\] \[=({{a}^{2}}{{b}^{2}}+4{{c}^{2}})[{{(ab)}^{2}}-{{(2c)}^{2}}]\] \[=({{a}^{2}}{{b}^{2}}+4{{c}^{2}})(ab+2c)(ab-2c)\]
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