Question

if 2a-3b =3 and ab =2, find the value of 8a3-27b3

Answer 1

Solution :

Now,

$8 {a}^{3} - 27 {b}^{3} \\ = {(2a - 3b)}^{3} + (3 \times 2a \times 3b\times(2a - 3b)) \\ = (2a - 3b)^{3} + 18ab(2a - 3b) \\ = {3}^{ 3} + 18 \times 2 \times 3 \\ = 27 + 108 \\ = 135$

[Ans.]