\(A=555\cdot554555-554\cdot555554\\ =555\cdot\left(554\cdot1000+555\right)-554\cdot\left(555\cdot1000+554\right)\\ =555\cdot554\cdot1000+555^2-555\cdot554\cdot1000-554^2\\ =\left(555\cdot554\cdot1000-555\cdot554\cdot100\right)+\left(555^2-554^2\right)\\ =555^2-554^2\\ =555^2-555\cdot554+555\cdot554-554^2\\ =555\cdot\left(555-554\right)+554\cdot\left(555-1\right)\\ =555+554\\ =1109\)
`A=555.554555-554.555554`
`=555.(555555-1000)-(555-1).555554`
`=555.555555-555.1000-555.555554+555554`
`=555.(555555-555554)-555000+555554`
`=555.1+554`
`=555+554=1109`