Question

What is the fourth term in the binomial expansion of (2x – y) 7?

Answer 1

`(7C4) (2x)^4 (-y)^(7-4)`

And replacing we got:

`35 (2^4) x^4 (-y)^(-3)`

And then the final term would be:

`-560 x^4 y^3`

Explanation:

For this case we have the following expression:

`(2x-y)^7`

And we can use the binomial theorem given by:

`(x+y)^n =\sum_(k=0)^n (nCk) x^k y^(n-k)`

And for this case we want to find the fourth term and using the formula we have:

`(7C4) (2x)^4 (-y)^(7-4)`

And replacing we got:

`35 (2^4) x^4 (-y)^(-3)`

And then the final term would be:

`-560 x^4 y^3`