Question

The second term of the expansion (3x-4y)^5 is

Answer 1

To solve this, we're going to have to use the binomial theorem. It states that:

$(x+y)^{n}=\sum_{k=0}^{n} \binom{n}{k}x^{n-k}y^k$

If you want a specific term, we can just disregard the polynomial and use this:

$A_k= \binom{n}{k-1}x^{n-k-1}y^{k-1}$

Where A_k is the kth term. In the context of this problem it would look like:

$A_2= \binom{5}{1}(3x)^{5-1}(-4y)^1= 5*81*-4*x^4*y=1620x^4y$

So, based on that, our second term is $1620x^4y$