Final answer:
The expression 8y³ - 27 can be factored using the difference of cubes formula to get (2y - 3)(4y² + 6y + 9), where 8y³ is (2y)³ and 27 is 3³.
Step-by-step explanation:
The student has asked us to factor the expression 8y³ - 27 completely. To tackle this problem, we will use the difference of cubes formula, which states that a³ - b³ = (a - b)(a² + ab + b²).
In this expression, 8y³ can be thought of as (2y)³ and 27 as 3³. Applying the difference of cubes formula, we get:
Therefore, the completely factored form of 8y³ - 27 is (2y - 3)(4y² + 6y + 9). When factoring expressions, remember to cube the digit term in the usual way and multiply the exponent of the exponential term by 3. Moreover, it is essential to eliminate terms where possible to simplify the algebra.