Answer
$2(3x-2y)(9x^2+6xy+4y^2)$
Work Step by Step
The formula for factoring the sum of two cubes is: $A^3+B^3=(A+B)(A^2-AB+B^2)$.
The formula for factoring the difference of two cubes is: $A^3-B^3=(A-B)(A^2+AB+B^2)$.
Hence here: $54x^3-16y^3=\\=2(27x^3-8y^3)\\=2((3x)^3-(2y)^3)\\=2(3x-2y)((3x)^2+(3x)(2y)+(2y)^2)\\=2(3x-2y)(9x^2+6xy+4y^2)$
