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    Question

    If 125x3 - 64y3 = (Ax + By)

    (Dy2 - Cx2 + 20xy) , then the value of A + C - 2B + 3D is:
    A 32 Correct Answer Incorrect Answer
    B 36 Correct Answer Incorrect Answer
    C 28 Correct Answer Incorrect Answer
    D 24 Correct Answer Incorrect Answer

    Solution

    125x3 - 64y3 = (Ax + By) (Dy2 - Cx2 + 20xy)

    (5x) 3 - (4y) 3 = (Ax + By) (Dy2 - Cx2 + 20xy)

    As we know,

    x3 - y3 = (x - y) (x2 + y2 + xy)

    So, (5x) 3 - (4y) 3 = (5x - 4y) (25x2 + 16y2 + 20xy) = (Ax + By) (Dy2 - Cx2 + 12xy)

    Comparing the coefficients of both sides, we get;

    'A' = 5, B = - 4, C = - 25, D = 16

    So, A + C - 2B + 3D = 5 - 25 - {2 X ( - 4) } + 3 X 16

    = - 20 + 8 + 48 = 36

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