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

D.) x3(2x + 5) + 4(2x + 5)Step-by-step explanation:...

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

msdsh03

10.03.2022

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

Step-by-step 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:

$\frac{n!}{\left(n-r\right)!\cdot r!}x^{\left(n-r\right)}\cdot y^r$

$=\frac{5!}{\left(5-3\right)!\cdot 3!}a^{\left(5-3\right)}\cdot (-b^2)^3$

$=\frac{5!}{\left(2\right)!\cdot 3!}a^{\left(2\right)}\cdot (-b^2)^3$

$=\frac{5!}{\left(2\right)!\cdot3!}a^2\cdot-b^6$

$=-\frac{120}{2\cdot6}a^2\cdot b^6$

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

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

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