Differential backup size is too large - sql

Question

I have a database on SQL Server 2008 R2 SP2, I have this backup plan on that db:
every Friday morning I get a full backup of my db and at noon I get differential backup and the other days of the week I get differential backup twice per day (morning and noon).
The full backup size is about 50 GB. My problem is: the first differential backup size is about 42 GB.
I have no jobs in the time between the full and differential backup and there is no any rebuild index, reorganize index or update stats and the transaction on this db is not more.
In order to test, I get a full backup from db and after this done, I get differential backup from that immediately but the differential backup size is about 42 GB.
Even if I check the DCM page content and after getting full backup this page is reset.
I don't know what is the problem.
Here are my backup commands:
Full backup:
BACKUP DATABASE [test]
TO DISK = N''filePath\test.bak''
WITH NOFORMAT, NOINIT, NAME = 'test', SKIP, REWIND,
NOUNLOAD,COMPRESSION, STATS = 10
DIFF Backup
BACKUP DATABASE [test]
TO DISK = N''filePath\test.bak''
WITH DIFFERENTIAL, NOFORMAT, NAME = 'testdiff', NOINIT, SKIP, REWIND,
NOUNLOAD, STATS = 10

Answer 1

You are specifying NOINIT clause.
Indicates that the backup set is appended to the specified media set, preserving existing backup sets. If a media password is defined for the media set, the password must be supplied. NOINIT is the default.
Your files will keep growing as new backups are being appended.
Also your post does not mention when and how you backup the log. I hope this is only an omission, as log needs to be backed up too.

Answer 2

BACKUP DATABASE [test] TO DISK = N''filePath\test.bak'' WITH DIFFERENTIAL, NOFORMAT, NAME = testdiff',NOINIT, SKIP, REWIND, NOUNLOAD, STATS = 10
in the Statement above I've used NOINIT, naturally the new backup file must be appended to the previous file but because I use the new name for my new backup file, the new file will be created and it won't appended to previous file.
But my problem has been solved. because I had replication on my DB before and after removing it the publication had remained in the SQL instance and there was an active transaction(Replication) on my db so it locks many of the transaction logs and many of my VLFs were active.they were waiting to send to subscriber server.
after removing publication from my SQL instance the VLF files set to 0 and the transaction log file has been shrink So, the differential backup file size were decreased.