If $5 x - 4 y = 7 a n d x y = 8$ , find : $125 x^{3} - 64 y^{3}$

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Solution

$125 x^{3} - 64 y^{3} = (5 x)^{3} - (4 y)^{3} = (5 x - 4 y)^{3} + 3 (5 x) (4 y) (5 x - 4 y) = (5 x - 4 y)^{3} + 60 x y (5 x - 4 y) = (7)^{3} + 60 (8) (7) = 343 + 3360 = 3703$

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