Answer: The factorization of the expression x^3 - 64 can be written as (x - 4)(x^2 + 4x + 16).
To understand how we arrive at this factorization, let's break it down step by step:
1. First, notice that 64 is equal to 4^3. So we can rewrite the expression x^3 - 64 as x^3 - 4^3.
2. We can apply the difference of cubes formula, which states that a^3 - b^3 can be factored as (a - b)(a^2 + ab + b^2). In this case, a is x and b is 4.
3. Using the difference of cubes formula, we have x^3 - 4^3 = (x - 4)(x^2 + 4x + 16).
So, the factorization of x^3 - 64 is (x - 4)(x^2 + 4x + 16).
This means that the expression can be written as the product of two factors: (x - 4) and (x^2 + 4x + 16).
It's important to note that this factorization is obtained by recognizing the pattern and applying the difference of cubes formula.