Final answer:
To rewrite the expression x⁴−64, recognize it as a difference of squares, and factor it into the product of two binomials: (x²+8)(x²−8).
Step-by-step explanation:
The question asks for an expression that shows one way to rewrite the expression x⁴−64. This expression can be factored because it is a difference of squares. A difference of squares is a binomial expression where each term is a perfect square, and the expression is in the form of a²−b², which can be factored into (a+b)(a−b).
In the case of x⁴−64, we can recognize that x⁴ (x raised to the fourth power) is the square of x² and 64 is the square of 8. Therefore, the expression can be rewritten as (x²+8)(x²−8), which shows its factorization into the product of two binomials.