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Might seem a little silly, but I just can't seem to get my head around it. In math, when we write (a + b)^2 = a^2 + 2ab + b^2 or 2 = 1 + 1 , we mean the quantity on the left side of = and the quantity on the right side of = are the same. In physics, when we write F = ma or E = mc^2, what's on the left side of = cannot a priori exist unless what's on the right side of = is given. I don't get how in physics, as does in math, the part on the left side of = and the part on the right side of = can represent the same quantity. Further, I don't get writing the unit of acceleration, which is m / s / s as m / s^2, simply for unit cancellation in manipulation of equations in physics. m / s / s has real world physics meaning. m / s^2 does not, because s^2 does not have meaning in the real world like s does. Is it me, or is notation used in physics somewhat sloppy and need new notations or symbols just for physics? Any help or explanation is greatly appreciated!

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