If 3x - 2y = 10 and xy = 11, the value of 27x3 - 8y3 is __________

Explanation

Given: 3x - 2y = 10 and xy = 11 Formula used: (a - b)3 = a3 - b3 - 3ab(a - b) Calculation: 3x - 2y = 10 Taking a cube on both sides of the above equation: (3x - 2y)3 = 103 ⇒ 27x3 - 8y3 - 3(3x)(2y)(3x - 2y) = 1000 ⇒ 27x3 - 8y3 - 18(xy)(3x - 2y) = 1000 Putting, 3x - 2y = 10, xy = 11 ⇒ 27x3 - 8y3 - 18 × 11 × 10 = 1000 ⇒ 27x3 - 8y3 - 1980 = 1000 ⇒ 27x3 - 8y3 = 1000 + 1980 = 2980 Hence, the value of 27x3 - 8y3 is '2980'.