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8th Class Mathematics Algebraic Expressions Question Bank Algebraic Expressions & Identities

  • question_answer
    If \[\left( 3x-2y \right)=5\] and \[\mathbf{xy}=\mathbf{6}.\]Find the value of \[~27{{x}^{3}}-8{{y}^{3}}\]

    A)  550                             

    B)  625            

    C)  665 

    D)  675

    Correct Answer: C

    Solution :

    (c): \[{{\left( 3x-2y \right)}^{3}}={{5}^{3}}\] \[\Rightarrow {{\left( 3x \right)}^{3}}-3\times 3x\times 2y\left( 3x-2y \right)-8{{y}^{3}}=125\] \[\Rightarrow 27{{x}^{3}}-18xy\left( 3x-2y \right)-8{{y}^{3}}=125\] \[=27{{x}^{3}}-18\times 6\times 5-8{{y}^{3}}=125\] \[\Rightarrow 27{{x}^{3}}-8{{y}^{3}}=125+540=665.\]


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