Answer:
Final answer is [tex]-10a^2 b^6[/tex].
Step-by-step explanation:
Given expression is [tex](a-b^2)^5[/tex].
Now we need to find the fourth term of the given expression [tex](a-b^2)^5[/tex]. So apply the nth term formula using binomial expansion.
exponent n=5
4th term means we use r=4-1=3
x=a, [tex]y=-b^2[/tex]
rth term in expansion of [tex](x+y)^n[/tex] is given by formula:
[tex]\frac{n!}{\left(n-r\right)!\cdot r!}x^{\left(n-r\right)}\cdot y^r[/tex]
[tex]=\frac{5!}{\left(5-3\right)!\cdot 3!}a^{\left(5-3\right)}\cdot (-b^2)^3[/tex]
[tex]=\frac{5!}{\left(2\right)!\cdot 3!}a^{\left(2\right)}\cdot (-b^2)^3[/tex]
[tex]=\frac{5!}{\left(2\right)!\cdot3!}a^2\cdot-b^6[/tex]
[tex]=-\frac{120}{2\cdot6}a^2\cdot b^6[/tex]
[tex]=-10a^2\cdot b^6[/tex]
Hence final answer is [tex]-10a^2 b^6[/tex].
