Solve the equation by factoring. \( 2 a^{2}-32=0 \) Select the correct choice below and fill in any answer boxes within your choice. A. The solution set is \( \{ \) \}. (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as neede B. There are no solutions.

First, let's solve the equation \( 2a^{2} - 32 = 0 \) by factoring. We can start by factoring out the common factor of 2: \( 2(a^{2} - 16) = 0 \) Next, we can further factor \( a^{2} - 16 \) since it is a difference of squares: \( 2(a - 4)(a + 4) = 0 \) Now, set each factor equal to zero: 1. \( a - 4 = 0 \) → \( a = 4 \) 2. \( a + 4 = 0 \) → \( a = -4 \) Therefore, the solution set is \( \{ -4, 4 \} \). Remember, a difference of squares is a powerful tool in factoring. It’s often used when two perfect squares are separated by a minus sign. In this case, we applied it to transform the quadratic into linear factors. If you're looking for more practice, try creating your own quadratic equations and applying the same method! It's a fantastic way to sharpen your factoring skills.