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SSC Sample Paper Mock Test-19 SSC CGL Tear-II Paper-1

  • question_answer
    The factors of \[({{a}^{2}}-{{b}^{2}})({{c}^{2}}-{{d}^{2}})({{c}^{2}}-{{d}^{2}})-4\,\,abcd\]are

    A)  \[(ac+bd+bc+ad)(ac-bd-bc-ad)\]

    B)  \[(ac-bd-bc+ad)(ac+bd+dc+ab)\]

    C)  \[(ac-bd+bc+ad)(ac-bd=-bc-ad)\]

    D)  \[(ac-bd-bc-ad)(ac+bd+dc+ab)\]

    Correct Answer: C

    Solution :

    \[({{a}^{2}}-{{b}^{2}})({{c}^{2}}-{{d}^{2}})-4abcd\] \[={{a}^{2}}{{c}^{2}}-{{a}^{2}}{{d}^{2}}-{{b}^{2}}{{c}^{2}}+{{b}^{2}}{{d}^{2}}-4abcd\] \[=({{a}^{2}}{{c}^{2}}+{{b}^{2}}{{d}^{2}}-2abcd)-({{b}^{2}}{{c}^{2}}+{{a}^{2}}{{d}^{2}}+2abcd)\] \[={{(ac-bd)}^{2}}-{{(bc+ad)}^{2}}\] \[=(ac-bd+bc+ad)(ac-bd-bc-ad)\]


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