Changes in the carrying amount of goodwill for the years ended December 31, 2020 and 2021 were as follows (in millions):


	Google		Google Services		Google Cloud		Other Bets		Total
Balance as of December 31, 2019	$	19,921	$	0	$	0	$	703	$	20,624
Acquisitions	204		53		189		0		446
Foreign currency translation and other adjustments	46		56		5		(2)		105
Allocation in the fourth quarter of 2020(1)	(20,171)		18,408		1,763		0		0
Balance as of December 31, 2020	0		18,517		1,957		701		21,175
Acquisitions	0		1,325		382		103		1,810
Foreign currency translation and other adjustments	0		(16)		(2)		(11)		(29)
Balance as of December 31, 2021	$	0	$	19,826	$	2,337	$	793	$	22,956

(1)Represents reallocation of goodwill as a result of our change in segments in the fourth quarter of 2020. See Note 15 for further details.


	As of December 31, 2020
	Gross Carrying Amount		Accumulated Amortization		Net Carrying Amount
Patents and developed technology	$	4,639	$	3,649	$	990
Customer relationships	266		49		217
Trade names and other	624		461		163
Total definite-lived intangible assets	5,529		4,159		1,370
Indefinite-lived intangible assets	75		0		75
Total intangible assets	$	5,604	$	4,159	$	1,445


	As of December 31, 2021
	Gross Carrying Amount		Accumulated Amortization		Net Carrying Value
Patents and developed technology	$	4,786	$	4,112	$	674
Customer relationships	506		140		366
Trade names and other	534		295		239
Total definite-lived intangible assets	5,826		4,547		1,279
Indefinite-lived intangible assets	138		0		138
Total intangible assets	$	5,964	$	4,547	$	1,417

Patents and developed technology, customer relationships, and trade names and other have weighted-average remaining useful lives of 0.7 years, 3.5 years, and 4.5 years, respectively.

For all intangible assets acquired and purchased during the year ended December 31, 2021, patents and developed technology have a weighted-average useful life of 4.1 years, customer relationships have a weighted-average useful life of 4.3 years, and trade names and other have a weighted-average useful life of 9.9 years.

Amortization expense relating to purchased intangible assets was $795 million, $774 million, and $875 million for the years ended December 31, 2019, 2020, and 2021, respectively.

As of December 31, 2021, expected amortization expense relating to purchased intangible assets for each of the next five years and thereafter was as follows (in millions):