Final answer:
To factor the given expression, we use the sum of cubes formula. Using the formula, the expression g(x) = 27x³ + 1 is factored as (3x + 1)(9x² - 3x + 1).
Step-by-step explanation:
To factor the expression a³ + b, we can use the sum of cubes formula. The formula states that a³ + b³ = (a + b)(a² - ab + b²). In this case, however, we don't have b³ but just b, so the formula simplifies to a³ + b = (a + b)(a² - ab + b²).
For the expression a³ - b, we can use the difference of cubes formula, which states that a³ - b³ = (a - b)(a² + ab + b²). Again, since we have a³ instead of a³ - b³, the formula simplifies to a³ - b = (a - b)(a² + ab + b²).
Now let's factor the given expression, g(x) = 27x³ + 1. Since we can rewrite 27x³ as (3x)³, we can use the sum of cubes formula to factor it out. Following the formula, we have g(x) = (3x + 1)(9x² - 3x + 1).
Therefore, the expression is factored as g(x) = (3x + 1)(9x² - 3x + 1).
Learn more about Factoring binomials