For homework questions what is the difference between being asked to verify something and being asked to prove something?

I've always been curious if there is a definite difference between the terms or if they just depend on the context of a problem.

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I thought they both are the same, but maybe verify is attached more to computation whereas prove this is attached more to the formal guidelines of a proof. –  Q.matin Mar 10 at 7:26
In most cases they’re pretty much the same. Verify can also be used of a computation checking a special case (verify that the formula yields the correct result when $n=1$) and in general tends to suggest that the result being verified is relatively straightforward (it’s easy to verify that this function is well-defined). –  Brian M. Scott Mar 10 at 14:23

I guess verify is more often used when the thing you need to prove is already given, but I don't think there is an essential one.

(I am German, maybe we use it a bit different)

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For example, a question might be asked as: Prove that $(a+b)^2 = a^2 + b^2 + 2ab$ and verify the statement with a=1,b=2.
However, you might also be asked to verify that $(a+b)^2=a^2+b^2+2ab$. –  Brian M. Scott Mar 10 at 14:18