Question

Can anyone find the fourth term of (a-b^2)^5 Please?

Answer 1

`-10a^(2) b^(6)`

Explanation:

For
`(a - b^(2) )^(5)`, use the 5th row of the Pascal Triangle to expand the binomial.

Apply the Binomial Theorem and simplify.

Count the number of terms and find the 4th term.

Answer 2

Final answer is
`-10a^2 b^6`.

Explanation:

Given expression is
`(a-b^2)^5`.

Now we need to find the fourth term of the given expression
`(a-b^2)^5`. So apply the nth term formula using binomial expansion.

exponent n=5

4th term means we use r=4-1=3

x=a,
`y=-b^2`

rth term in expansion of
`(x+y)^n` is given by formula:

`(n!)/(\left(n-r\right)!\cdot r!)x^(\left(n-r\right))\cdot y^r`

`=(5!)/(\left(5-3\right)!\cdot 3!)a^(\left(5-3\right))\cdot (-b^2)^3`

`=(5!)/(\left(2\right)!\cdot 3!)a^(\left(2\right))\cdot (-b^2)^3`

`=(5!)/(\left(2\right)!\cdot3!)a^2\cdot-b^6`

`=-(120)/(2\cdot6)a^2\cdot b^6`

`=-10a^2\cdot b^6`

Hence final answer is
`-10a^2 b^6`.