Answer:
The third term of the expansion [tex](a+b)^n[/tex] is [tex]C(n,2)\cdot a^{n-2}\cdot b^{2}[/tex].
Step-by-step explanation:
According to the binomial expansion,
[tex](a+b)^n=C(n,0)a^{n}+C(n,1)a^{n-1}b+...+C(n,n)b^n[/tex]
So, the rth term of this expansion is
[tex]C(n,r-1)a^{n-r+1}b^{(r-1)}[/tex]
We have to find the third term of the expansion [tex](a+b)^n[/tex] is
[tex]C(n,3-1)a^{n-3+1}b^{(3-1)}[/tex]
[tex]C(n,2)\cdot a^{n-2}\cdot b^{2}[/tex]
Therefore the third term of the expansion [tex](a+b)^n[/tex] is [tex]C(n,2)\cdot a^{n-2}\cdot b^{2}[/tex].
