This might be a basic question but I am a little confused.
I have some lecture notes that says calcium phosphate ($\ce{Ca3(PO4)2}$) reacts with calcium hydroxide ($\ce{Ca(OH)2}$) to form Hydroxyapatite ($\ce{Ca10(PO4)6(OH)2}$).
So, the chemical formula (even when unbalanced) should be:
$$\ce{Ca3(PO4)2 + Ca(OH)2 -> Ca10(PO4)6(OH)2}$$
I can't figure out why $\ce{Ca10(PO4)6(OH)2}$ is the product of $\ce{Ca3(PO4)2}$ and $\ce{Ca(OH)2}$ and I am having trouble balancing it (see below). On Sigma Aldrich's website, it says the linear Formula for hydroxyapatite is $\ce{3Ca3(PO4)2·Ca(OH)2}$. I copied and pasted this directly. I assume the dot between the calcium phosphate and calcium hydroxide means 'plus'.
On the Sigma Aldrich's website, the calcium phosphate is written/balanced as $\ce{3Ca3(PO4)2}$, whereas the lecture notes I have are just $\ce{Ca3(PO4)2}$. Even with the three in front as the coefficient, I get $\ce{9Ca + Ca -> Ca10}$, $\ce{(PO4)2}$ and $\ce{(OH)2}$ which is $\ce{Ca10(PO4)2(OH)2}$, instead of $\ce{Ca10(PO4)6(OH)2}$. If I use the formula in my lecture notes, I get $\ce{Ca3(PO4)2 + Ca(OH)2 -> Ca4(PO4)2(OH)2}$, which is even more off.
Should it be $\ce{3(Ca3(PO4)2)}$ instead of $\ce{3Ca3(PO4)2}$ so the coefficient 3 can be applied to the subscript 2 on the $\ce{PO4}$ to give $\ce{(PO4)6}$?
What am I missing?