Final answer:
The correct response is option '(+9)', which represents the difference of two squares and can be factored as (3 + 3)(3 - 3), aligning with the exponent rule x^p * x^q = x^(p+q).
Step-by-step explanation:
The correct answer is option '(+9)'. The difference of two squares refers to an expression of the form a^2 - b^2, which can be factored into (a + b)(a - b). In the options provided, (+9) or more clearly written as 3^2 - 3^2, fits this form, because it is equivalent to (3 + 3)(3 - 3).
This is an example of the difference of two squares because we have the product of two terms, (3) and (9), with opposite signs. The difference of two squares can be written as (a+b)(a-b), where 'a' and 'b' represent any two terms. In this case, 'a' is 3 and 'b' is 9, so we have (3+9)(3-9).
This is because the exponent rule of adding exponents applies when you multiply powers with the same base, as in x^p * x^q = x^(p+q). Note that when factoring the difference of two squares, it is crucial to identify terms that are perfect squares and to remember that the square of a number is always positive, whether the number is positive or negative.