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SSC Quantitative Aptitude Algebra Question Bank Elementary Algebra (II)

  • question_answer
    \[{{(y-z)}^{3}}+{{(z-x)}^{3}}+{{(x-y)}^{3}}\]is equal to

    A) \[3\,\,(y-z)(z+x)(y-x)\]

    B) \[(x-y)(y+z)(x-z)\]

    C) \[3\,(y-z)(z-x)(x-y)\]

    D) \[(y-z)(z-x)(x-y)\]

    Correct Answer: C

    Solution :

    [c] Suppose, \[y-z=a,\]\[z-x=b\]and \[x-y=c\] \[\therefore \]      \[a+b+c=0\] \[\Rightarrow \]   \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}=3abc\] \[=3\,(y-z)(z-x)(x-y)\]


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