A single displacement reaction, also called as a single-replacement reaction, is one where one element replaces another similar element in a compound. The general form is:$^2$
$$ \text{A + BC} \rightarrow \text{AC + B} $$
In this general reaction, A is a metal replacing B, also a metal, in the compound. However, what if the element that is doing the replacement is non-mental? This is the general form for that.$^2$
$$ \text{Y + XZ} \rightarrow \text{XY + Z} $$
In this general reaction, X is a non-mental replacing Z, also a non-mental, in the compound.$^2$
When a strip of Magnesium metal is placed in an aqueous solution of copper(II) nitrate, it replaces the copper.$^2$
$$ \text{Mg}(s)\text{ + Cu(NO}_3\text{)}_2(aq) \rightarrow \text{Mg(NO}_3\text{)}_2(aq) \text{ + Cu}(s) $$
A double-displacement reaction, also known as double-replacement, is when the positive and negative ions of two ionic compounds exchange their places to form two new compounds. The general form is:$^2$
$$ \text{AB + CD} \rightarrow \text{AD + CB} $$
Where A and C are cations while B and D are anions.$^2$ Double-displacement reactions generally happen in aqueous solution.$^2$
$$ \text{2Kl}(aq)\text{ + Pb(NO}_3\text{)}_2 $$
A synthesis reaction, also known as a combination reaction, is when two or more substances combine to create a single new substance. This is the general form.$^2$
$$ \text{A}+\text{B}\rightarrow \text{AB} $$
This is an example of sodium reacting with chlorine to form Sodium Chloride.$^2$
$$ \text{2Na(}s\text{) + Cl}_2(g) \rightarrow \text{2NaCl(}s) $$
A common synthesis reaction that takes place is the reaction of an element with oxygen to form an oxide. Both metals and non-metals react with oxygen in most conditions. For example, Magnesium and oxygen.$^2$