Question

How do you find the 7th term in the expansion of the binomial `(7x+2y)^15`?

Answer 1

`7` th term is `15C_6* (7x)^9*(2y)^6 = 1.29E+13*x^9*y^6`

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=7x ; b=2y , n= 15)`

We know `nC_r= (n!)/(r!(n-r)!) :. 15C_6=5005`

`7` th term is `15C_6* (7x)^9*(2y)^6 = 1.29E+13*x^9*y^6` [Ans]