I noticed that the words זֶה אֱלֹהֶיךָ from the verse of Nehemiah 9:18 describing the Golden Calf are often translated as: 'This is your G-d'. But Exodus 32:4 and 32:8 speak of אֵלֶּה אֱלֹהֶיךָ which are often translated as 'These are your gods'. Why the difference if there was only one idol (golden calf) made?
Here is some of the commentary on that phrase from sefaria, starting from one simple claim, of the Bekhor SHor that they were using a divine plural,
דרך לדבר אלהות ואדנות בלשון רבים כמו אלהים קדושים
The Ohr Hachayim writes,
When they spoke about אלה, "These," they made sure that they did not exclude G'd in Heaven. Possibly, they used the expression העלוך "they brought you up," to hint that there was a Power on earth which equals the Power in the Heavens, G'd forbid;
Whereas the Rabbeinu Bahya writes that this was about adding something to a pantheon of figures,
You have to realise that when the Israelites said: “these are your gods O Israel, who brought you out of Egypt,” there would have been nothing wrong with this if what they had in mind had been the same as what Aaron had in mind when making the calf. After all, we have already explained that Exodus 14,19 accorded the title “elohim” to a column of cloud and a column of fire; there was therefore nothing inherently wrong in the use of the word אלוהים or אלוהיך.
Our sages in Sanhedrin 63 derive from this that these Israelites strove to have many deities. They derive this from the word אלה “these,” instead of זה, “this,” if they had referred only to the golden calf. We do indeed find the latter expression in Nechemyah 9,18: זה אלוהיך אשר העלוך ממצרים, “this is your god who took you out of Egypt.”
The Torah Temima cites an opinion that there were multiple calves made, one for each tribe, though they all looked alike
אלה אלהיך וגו׳. תניא, ר׳ שמעון בן יוחאי אומר, י"ג עגלים עשו ישראל ואחד דמוסיא לכולן זכלומר י"ב עגלים עגל לכל שבט ושבט ואחד היה משותף לכל השבטים ביחד, ודמוסיא הוא הנהגה כללית בלשון רומי. דכתיב אלה אלהיך ישראל אשר העלוך הרי י"ב שבטים, וכתיב (נחמיה ט׳:י״ח) זה אלהיך אשר העלך, הרי דמוסיא אחד לכולן חכונת הדרשה ליישב סתירת הלשונות דכאן כתיב אלה אלהיך אשר העלוך, בלשון רבים, ובנחמיה כתיב זה אלהיך אשר העלך בלשון יחיד, ודרשו שזה שנאמר בלשון רבים מוסב על מאמר כל שבט לעגל שלו, ומה שנאמר בלשון יחיד מוסב על מאמר כל העם להעגל המשותף, ועיין בויק"ר פ' ה' ובדרשה הבאה. . (ירושלמי סנהדרין פ"י ה"ב)
Another interesting discrepancy -- Exodus says these are your gods, Israel, who took you out...; Nehemiah reads this is your god who took you out.
The simplest suggestion would be that "god" is acceptable in Hebrew in both singular and plural; or perhaps it was more commonly plural in earlier Hebrew and changed in later Hebrew.
Alternatively: the narrative in Exodus is hinting at all kinds of complexities that actually went into the golden calf, such as multiple calves for multiple tribes; and the involvement of the erev rav (as the Kli Yakar points out -- if the audience is addressed as "Israel", that would imply the speakers are not Israel).
When Nehemiah is recapping Jewish history to get the Second Temple going, he needs to drive home a few points. At this moment in history, there is just one Jewish people; he can't afford blaming the quasi-Jews (especially not when the "bluebloods" stayed behind in Babylon; a whole mishmash of pedigrees returned to Israel), and he certainly can't afford any nods to divisions between the tribes -- that had turned out disastrously during the First Temple period -- you'll notice the North/South split is completely glossed over in Nehemiah Chapter 9. So for the sake of what the Jews need to know for their new existence in Israel, the focus is simplified -- one golden calf that the Jews made.