Answer:
The fourth term is [tex]5940x^9.[/tex]
Step-by-step explanation:
We use the binomial theorem which says:
[tex](x+y)^n = \sum_{k=0}^n (nCk) \:x^{n-k}y^k[/tex]
Where
[tex](nCk)=\frac{n!}{k!(n-k)!}.[/tex]
For [tex](x+3)^{12}[/tex]
The theorem gives:
[tex](x+3)^{12}= \sum_{k=0}^{12}(12Ck) \:x^{12-k}*3^k[/tex]
From this the fourth term is when [tex]k=4:[/tex]
[tex](12C3)x^{12-3}*3^3[/tex]
Since [tex](12C3)=220[/tex]
[tex](12C3)x^{12-3}*3^3=\boxed{5940x^9}[/tex]
