8th Class Mental Ability Algebra Question Bank Algebra

  • question_answer The product of \[\left( \mathbf{3}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{2}}} \right)\] and \[\left( \mathbf{2}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+3}{{\mathbf{y}}^{\mathbf{2}}} \right)\] is_____.

    A) \[{{x}^{3}}+10{{x}^{2}}{{y}^{3}}+3{{y}^{4}}\]

    B) \[3{{x}^{2}}+5{{x}^{5}}{{y}^{2}}+3{{y}^{4}}\]

    C) \[6{{x}^{5}}+10{{x}^{2}}{{y}^{3}}+3{{y}^{4}}\]          

    D) \[6{{x}^{4}}+11{{x}^{2}}{{y}^{2}}+3{{y}^{4}}\]

    E) None of these

    Correct Answer: D

    Solution :

    Explanation Option [d] is correct. \[\left( 3{{x}^{2}}+{{y}^{2}} \right)\left( 2{{x}^{2}}+3{{y}^{2}} \right)=6{{x}^{4}}+9{{x}^{2}}{{y}^{2}}+2{{x}^{2}}{{y}^{2}}+3{{y}^{4}}=6{{x}^{4}}+11{{x}^{2}}{{y}^{2}}+3{{y}^{4}}\]

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