Factor the polynomial using a special factorization. \[ 54 x^{3}+2 y^{3} \] Answer

Step 1 ：The given expression is a sum of two cubes. The sum of cubes can be factored using the formula: \(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\)

Step 2 ：In the given expression \(54 x^{3}+2 y^{3}\), we can identify \(a = (54x^3)^{1/3} = 3x\) and \(b = (2y^3)^{1/3} = y\)

Step 3 ：Substitute these values into the formula to factor the expression

Step 4 ：The factored form of the polynomial \(54 x^{3}+2 y^{3}\) is \[2(3x + y)(9x^2 - 3xy + y^2)\]

Step 5 ：\(\boxed{2(3x + y)(9x^2 - 3xy + y^2)}\) is the final answer