Question

2a-3b=3 and ab=2,find the value of 8a cube -27b cube

Answer 1

$\textbf{ Hello Mate! }$

2a - 3b = 3 ( Given )

And, ab = 2 ( Given )

${(2a - 3b)}^{3} = {3}^{3} \\ \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) \\ \\ 8 { a }^{3} - 27 {b}^{3} - 3(2a)(3b)(2a - b) = 27 \\ \\ 8 {a}^{3} - 27 {b}^{3} - 18(2)(3) = 27 \\ \\ 8 {a}^{3} - 27 {b}^{3} = 27 + 108 \\ \\ 8 {a}^{3} - 27 {b}^{3} = 135$

Have great future ahead!