Question

2a - 3 v is equal to 3 and a b is equal to 2 find a 8 a cube minus 27 b cube

Answer 1

$2a - 3b = 3 \\ ab = 2 \\ {4a}^{2} + {9b}^{2} = {(2a - 3b)}^{2} + 2(2a)(3b) \\ = {3}^{2} + 12ab = 9 + 12 \times 2 = 9 + 24 \\ = 33 \\ {8a}^{3} - {27b}^{3} = {(2a)}^{3} - {(3b)}^{3} \\ = (2a - 3b)( {4a}^{2} + {9b}^{2} + 6ab ) \\ = 3(33 + 6 \times 2) \\ = 3 \times 45 \\ = 145$