how to simplify ?

General substitution for simplifying expressions

Simplify (b+1)^3

Explain how you can be sure that a fraction is simplified.

Explain how you can be sure that a fraction is simplified.

The simplified form of the circuit : is

The simplified circuit for the following circuit is

The simplified circuit for the following circuit is

Simplify the following circuit so that new circuit has minimum number of switches. Also draw simplified circuit.

which of the following when simplified vanishes