[tex]Identity: \\ \boxed{ {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2}) } \\ \\ 64 {x}^{9} - 125 {y}^{6} \\ \\ = {(4 {x}^{3} )}^{3} - {(5 {y}^{2} )}^{3} \\ \\ = (4 {x}^{3} - 5 {y}^{2} )( \: {(4 {x}^{3} )}^{2} + 4 {x}^{3} \times 5 {y}^{2} + {(5 {y}^{2} )}^{2} \: ) \\ \\ = (4 {x}^{3} - 5 {y}^{2} )(16 {x}^{6} + 20 {x}^{3} {y}^{2} + 25 {y}^{4} )[/tex]
