Final answer:
Multiplying the binomials (x-3)(x+3) using the FOIL method, the terms +3x and -3x cancel each other out, leaving x^2 - 9 as the result. Therefore, the correct answer is a) x^2 - 9.
Step-by-step explanation:
The multiplication of the binomials (x-3)(x+3) is performed using the FOIL method, which stands for First, Outer, Inner, and Last. This refers to the pairs of terms from each binomial that we multiply together. Let's apply this method step by step:
First: Multiply the first terms in each binomial, which is x times x, to get x^2.
Outer: Multiply the outer terms, which is x times 3, resulting in +3x.
Inner: Multiply the inner terms, which is -3 times x, resulting in -3x.
Last: Multiply the last terms in each binomial, which is -3 times 3, to get -9.
When we combine these results, +3x and -3x cancel each other out because they are opposite in sign. This leaves us with x^2 - 9 as the final result.
So the correct answer is a) x^2 - 9.