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8th Class Mathematics Factorisation Question Bank Factorization

  • question_answer
    Factorize the given expression \[~\mathbf{mn}({{\mathbf{u}}^{\mathbf{2}}}+{{\mathbf{v}}^{\mathbf{2}}})-\mathbf{uv}\left( {{\mathbf{m}}^{\mathbf{2}}}+{{\mathbf{n}}^{\mathbf{2}}} \right)\]

    A)  \[\left( un+vm \right)\left( um-vn \right)\]                 

    B)  \[\left( un+vm \right)\left( um+vn \right)\]

    C)  \[\left( un-vm \right)\left( um-vn \right)\] 

    D)  \[\left( un-vm \right)\left( um+vn \right)\]

    Correct Answer: C

    Solution :

    (c): \[mn({{u}^{2}}-{{v}^{2}})-uv\,({{m}^{2}}+{{n}^{2}})\] \[={{u}^{2}}mn+{{v}^{2}}mn\] \[=-\,uv{{m}^{2}}-uv{{n}^{2}}\] \[=un\left( um-vn \right)+vm\left( vn-um \right)\] \[=un\left( um-vn \right)-vm\left( um-un \right)\] \[=\left( un-vm \right)\left( um-vn \right).\]


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