Final answer:
To factor the polynomial y³ - 512, we can use the formula for the difference of two cubes. The factored form of the polynomial is (y - 8)(y² + 8y + 64).
Step-by-step explanation:
To factor the polynomial y³ - 512 using the formula for the difference of two cubes, we can rewrite it as (y - 8)(y² + 8y + 64). To apply the formula, we need to understand that y³ - 512 can be expressed as (y - 8)(y² + 2y√3 + 4√3²), where √3 represents the square root of 3. However, in this case, we can simplify y² + 2y√3 + 4√3² to y² + 8y + 64 since 3² equals 9.