Genesis 30:4-5 - Did Jacob also get married to the servant girls of Leah and Rachel because they are called his wives?

When Jacob got married to Rachel and Leah each of them was given a woman to be her personal servant.  In Genesis 30:4-5 Rachel chooses to give her servant girl, Bilhah, as a wife to Jacob so that Rachel could bear children through her servant girl since Rachel was childless.  The Hebrew word for "wife" here is the same word as the one that is used when Leah and Rachel get married to Jacob in a marriage celebration.  So, how is the servant girl, Bilhah, called a wife just like Rachel, her mistress, when Bilhah was never "married" to Jacob in an official, cultural ceremony?

The Hebrew word that is translated "wife" in Genesis 30:5 has the general meaning of woman or womanhood.  It gets the meaning of "wife" from its use in a particular context.  So, when Rachel and Leah got married to Jacob they were called wives not only because they were married but because of that marriage they would have sexual relations with their husband Jacob.  When Bilhah is given to Jacob as a "wife" even though there is no marriage ceremony or celebration she is being given as a sexual partner for the purpose of producing offspring and this makes her a wife to Jacob.