Answer:
The coefficient of the fifth term is 126.
Step-by-step explanation:
The question implies that after the expansion of [tex](a+b)^{9}[/tex], what would be the coefficient of the fifth term. This long expansion can be easily done by the application of the Pascal principle of expansion.
Thus,
[tex](a+b)^{9}[/tex] = [tex]a^{9}[/tex] + [tex]9a^{8}b[/tex] + [tex]36a^{7} b^{2}[/tex] + [tex]84a^{6}b^{3}[/tex] + [tex]126a^{5}b^{4}[/tex] + [tex]126a^{4} b^{5}[/tex] + [tex]84a^{3} b^{6}[/tex] + [tex]36a^{2} b^{7}[/tex] + [tex]9ab^{8}[/tex] + [tex]b^{9}[/tex]
So, from this expansion, the fifth term is [tex]126a^{5}b^{4}[/tex]. And its coefficient is 126.
