Question

Factorise 64a cube- 27b cube - 144 a square b .......

Answer 1

$64 {a}^{3} - 144{a}^{2} b + 108a {b}^{2} - 27 {b}^{3} \\ 64 {a}^{3} - 48{a}^{2} b + 36a {b}^{2} - 27 {b}^{3} - 96 {a}^{2} b + 72a {b}^{2} \\ {(4a)}^{3} - {(4a)}^{2} \times 3 b + 3a \times {(4b)}^{2} - {(3b)}^{3} - 24ab(4a - 3b) \\ = {(4a - 3b)}^{3} - 24ab(4a - 3b) \\ = (4a - 3b)( \: {(4a - 3b)}^{2} - 24ab \: )$