Question

What is the 3rd term in the expansion of (3m^4-1)^4?

Answer 1

3rd term in expansion of `(color(red)3m^4-1)^4=54m^8`

Explanation:

Binomial theorem:
`(a-b)^n=nC_0a^nb^0-nC_1a^(n-1)b^1+nC_2a^(n-2)b^2-+...(-1)^n*nC_na^0b^n`.We have,`(3m^4-1)^4rArra=3m^4,b=1,n=4`,
Now,(r+1)th term in the expansion of `(a-b)^n is,color(red)(T_(r+1)=(-1)^n*nC_r*a^(n-r)*b^r)`
For 3rd term r+1=3`rArr`r=2
`rArrT_(2+1)=(-1)^4*4C_2*(3m^4)^(4-2)*(1)^2`
`rArrT_3=4C_2(3m^4)^2=(4*3)/(2*1)(3^2m^8)=6*9m^8=54m^8`