Question

if 2x -5y =2, xy = 12, find the value of 8x ^3-125y^3​

Answer 1

Answer:

728

Step-by-step explanation:

$2x - 5y = 2 \\ yx = 12 \\ 8 {x}^{3} - 125 {y}^{3} = ? \\ {(2x - 5y)}^{3} =( 2x) {}^{3} - (5y) {}^{3} - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 3 \times 2x \times 5y(2x - 5y) \\ (2) {}^{3} = 8x {}^{3} - 125y {}^{3} 9 - \\ \: \: \: \: \: \: \: \: \: \: \: \: (3 \times 2 \times 5)(xy)(2) \\ 8 = 8x {}^{3} - 125y {}^{3} - 60 \times 12 \\ 8 + 720 = 8x {}^{3} - 125y {}^{3} \\ 728 = 8x {}^{3} - 125y {}^{3}$

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