• Both and both the are used in the same way in reference to two particular persons or things.

EXAMPLE: Both books discuss the possibility of third world war.
EXAMPLE: Both the books discuss the possibility of third world war.

• Both is used after an auxiliary verb, or after an auxiliary verb but before the main verb.

EXAMPLE: We are both regular partners in tennis.
EXAMPLE: They have both started to learn English together.

• Both is used after a modal (e.g. can, could, may, might, etc.)

EXAMPLE: They can both speak five languages.

• Both is used before the main verb

EXAMPLE: The pythons both escaped from their cage late last night.

• Both is used as subject in a sentence.

EXAMPLE: Both of us have been quarrelling since this morning.

• Both is used as object in a sentence.

EXAMPLE: I think I have fallen in love with both of you.

• We can use of or without of after both when we are specific about what or who we are referring to.

EXAMPLE: We recognize both of the men responsible for the crime.
EXAMPLE: We recognize both the men responsible for the crime.
EXAMPLE: We recognize both men responsible for the crime.