Question

How do you find the third term of `(4x-2/x)^8`?

Answer 1

Third term is `458752 x^4`

Explanation:

Binomial theorem:
`(a + b)^n =(nC_0) a^nb^0+ (nC_1) a^(n-1)b^1 +(nC_2) a^(n-2)b^2 +...... (nC_n)b^n`
Here `a=4x ; b=-2/x , n= 8`

We know `nC_r= (n!)/(r!(n-r)!) :. 8C_2=(8*7)/2=28`

`3` rd term is `T_3= 8 C_2 * (4x)^(8-2) * ( -2/x)^2` or

`T_3 = 28 * 4^6 * x^6 * 2^2 * 1/x^2 = 28* 4^7 * x^4` or

`T_3= 458752 x^4`

Third term is `458752 x^4` [Ans]