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FullSimplify gives me two different results for similar expressions

exp1 = Sqrt[((a (b+m (c-2 d)^2)^2)/(m (c-2d)^2))];
exp2 = exp1 /. {b -> b1 + b2};
FullSimplify[exp1, {m > 0, a > 0, b > 0, c > 2 d, d > 0}]
FullSimplify[exp2, {m > 0, a > 0, b1 > 0, b2 > 0, c > 2 d, d > 0}]

Can someone explain why it is so?

Anjan Kumar
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    Simplification can be finicky; it may stop at a "good enough" level. Consider also that what expression is to be considered simpler is sometimes in the eye of the beholder. In your case, it appears that you can nudge the second simplification in the direction you want by using PowerExpand on exp2, i.e. FullSimplify[ PowerExpand@exp2, yourConditions]. You might also be interested in this discussion: Advice for Mathematica as a mathematician's aid and 4522. – MarcoB Jan 23 '17 at 01:51

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