Answer:
According to the sum of cubes formula, Janis is correct
Step-by-step explanation:
The sum of cubes formula is given as follows;
x³ + y³ = (x + y)·(x² - x·y + y²)
The given expression is presented as follows;
27·x³ + 8
The given expression can be expressed as 27·x³ + 8 = (3·x)³ + 2³
Therefore, using the sum of cubes formula, we have;
(3·x)³ + 2³ = (3·x + 2)·((3·x)² - 3·x·2 + 2²) = (3·x + 2)·(9·x² - 6·x + 2²)
∴ 27·x³ + 8 = (3·x)³ + 2³ = (3·x + 2)·(9·x² - 6·x + 2²)
Therefore, Janis is correct, by the sum of cubes formula, we get;
27·x³ + 8 = (3·x + 2)·(9·x² - 6·x + 2²).
