At
https://reference.wolfram.com/language/ref/Around.html
under 'Properties & Relations' there is just the same operation you are asking about:
Around[10, 1]^2
According to this: (x+y)^2=x^2+2xy+y^2,
computing (1.2+0.1)^2=1.2^2+21.20.1+0.1^2
Let 0.1=delta, then
( 1.2 + 0.1 )^2= 1.2^2 + 2 * 1.2 * delta + delta^2
Around makes a first order series approximation, i.e. the highest delta power is 1, and you can check that 2 * 1.2 * 0.1=0.24, no 0.1^2 added to it.
I Hope this helps.
