Final answer:
The sum of two squares, unlike the difference of two squares, cannot be factored over the real numbers because no real numbers squared can yield a negative result to use a similar factoring pattern.
Step-by-step explanation:
Difference and Sum of Squares
The factoring of the difference of two squares follows a recognizable pattern where a² - b² can be factored into (a + b)(a - b). However, the sum of two squares does not have a similar factorization in the realm of real numbers. The expression a² + b² is not factorable over the real numbers because there are no real numbers that can be squared to yield a negative result, which would be necessary to use a similar factoring pattern as the difference of squares.
The correct answer to the question is c) The sum of two squares is not factorable. This is because a sum of squares does not produce factors that are expressible as linear polynomials with real coefficients.