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"Expediente" is a form of "expediente", a noun which is often translated as "record". "Indagación" is a noun which is often translated as "investigation". Learn more about the difference between "indagación" and "expediente" below.
la indagación(
een
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dah
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gah
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syohn
)A feminine noun is almost always used with feminine articles and adjectives (e.g., la mujer bonita, la luna llena).
1. (general)
a. investigation 
La policía reunió a los testigos e inició una indagación.The police gathered the witnesses and launched an investigation.
b. inquiry 
Los detectives realizaron indagaciones e interrogatorios pero no consiguieron información relevante.The detectives carried out inquiries and interrogations but were unable to obtain relevant information.
el expediente(
ehks
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peh
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dyehn
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teh
)A masculine noun is used with masculine articles and adjectives (e.g., el hombre guapo, el sol amarillo).
a. record 
El jefe del personal quiere revisar mi expediente académico antes de contratarme.The personnel manager wants to review my academic record before hiring me.
b. file 
Por haber perdido el expediente del paciente, los doctores no pudieron realizar la cirugía.Because they lost the patient's file, the doctors were unable to perform the surgery.
2. (legal)
a. disciplinary proceedings 
Al jefe acusado de acoso le incoaron expediente.Disciplinary proceedings were initiated against the manager accused of harassment.
b. inquiry 
Se abrirá un expediente en cuanto a esas acusaciones.An inquiry will be opened in relation to these allegations.
An adjective is a word that describes a noun (e.g., the big dog).
4. (old-fashioned) (opportune)
A word or phrase that is seldom used in contemporary language and is recognized as being from another decade, (e.g., cat, groovy).
a. expedient 
Yo estaba extremadamente agradecido que ella llegara en un momento tan expediente.I was extremely grateful that she arrived at such an expedient moment.