Question

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

Answer 1

Answer:

$2a - 3b = 3$

$ab = 2$

$8 {a}^{3} - 27 {b}^{3}$

${(2a - 3b)}^{3} = {3}^{3}$

$8 {a}^{3} - 27 {b}^{3} - \: 18ab(2a - 3b) = 27$

$8 {a}^{3} - 27 {b}^{3} - \: 18 \times 2(3) = 27$

$8 {a}^{3} - 27 {b}^{3} = 27 + 108$

$8 {a}^{3} - 27 {b}^{3} = 135$