Final answer:
The correct factored form of 27x^3+y^6 is (3x + y^2)(9x^2 - 3xy^2 + y^4), using the sum of cubes formula. This does not match any of the given options.
Step-by-step explanation:
The expression that is the completely factored form of 27x^3+y^6 is not explicitly provided among the options A), B), C), or D).
However, the correct factored form can be achieved by recognizing that the 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). In this case, a is (3x) and b is y^2.
Therefore, the factored form is (3x + y^2)(9x^2 - 3xy^2 + y^4), which does not match any of the given options.
When encountering an expression like 27x^3, we must cube the individual terms properly. Cubing of exponentials involves cubing the coefficient and multiplying the exponent by 3. Similarly, y^6 is already in cubic form as (y^2)^3, indicating it is the cube of y^2.