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SSC Quantitative Aptitude Algebra Question Bank Elementary Algebra (II)

  • question_answer
    \[x+y=z,\]then the expression \[{{x}^{3}}+{{y}^{3}}-{{z}^{3}}+3xyz\] will be equal to

    A) \[0\]

    B) \[3xyz\]

    C) \[-\,3xyz\]

    D) \[{{z}^{3}}\]

    Correct Answer: A

    Solution :

    [a] Given,          \[x+y=z\] \[\therefore \]      \[x+y+(-z)=0\] We know that, if \[a+b+c=0\]then \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}=3abc\] Here,\[x+y+(-z)=0\] \[\therefore \]      \[{{x}^{3}}+{{y}^{3}}-{{z}^{3}}=3xy\,(-z)\] \[\Rightarrow \]   \[{{x}^{3}}+{{y}^{3}}-{{z}^{3}}+3xyz\]


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