Answer:
[tex]C^{12}_7(3x)^5(-2)^7[/tex]
Step-by-step explanation:
Use binomial expansion formula:
[tex](a+b)^n=\sum \limits _{k=0}^nC^n_ka^{n-k}b^{k}[/tex]
Then
[tex](3x-2)^{12}=\sum \limits_{k=0}^{12}C_k^{12}(3x)^{12-k}(-2)^k[/tex]
In the expansion [tex](3x-2)^{12},[/tex] the term in [tex]x^5[/tex] is determined for
[tex]12-k=5\\ \\-k=5-12\\ \\-k=-7\\ \\k=7,[/tex]
then the coefficient at [tex]x^5[/tex] is
[tex]C^{12}_7(3x)^{12-7}(-2)^7=C^{12}_7(3x)^5(-2)^7[/tex]
