Digital logic simplification

1. The problem statement, all variables and given/known data and 3. The attempt at a solution
Simplify the equation in the following picture using karnaugh.

I divided it into two cases, one I used the square and the other I used the 2×1. Will either method work to get the solution, or is the 2×2 better since it is more simplified?

Let’s say I wanted to simplify the case 2 solution to get case 1 without karnaugh, how would I got about doing this?

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