And since radius is half the diameter, that becomes 1/4 when squared, and then it's also distributed across addition, then it also gets canceled. So basically, if you want to see what has more speaker area, just add up the square of the diameters for your comparison.
For instance, a 2x15" has less speaker area than a 4x12" because 15^2 + 15^2 = 450 and 12^2 + 12^2 + 12^2 + 12^2 = 576 and 450 < 576. HOWEVER, your average 2x15" cabinet is a lot deeper and bigger than a single 4x12", and your average 15" is more efficient than your average 12" speaker, so you have to consider all these different things when you think about how much air you're moving.
As for showing work, real mathematicians don't consider those steps to be worth showing.
For instance, a 2x15" has less speaker area than a 4x12" because 15^2 + 15^2 = 450 and 12^2 + 12^2 + 12^2 + 12^2 = 576 and 450 < 576. HOWEVER, your average 2x15" cabinet is a lot deeper and bigger than a single 4x12", and your average 15" is more efficient than your average 12" speaker, so you have to consider all these different things when you think about how much air you're moving.
As for showing work, real mathematicians don't consider those steps to be worth showing.