Question

Find the eleventh term in the expansion: (3x – 2y) ^15

Answer 1

We will have the following:

We are given the expression:

`(3x-2y)^(15)`

Now, we know that the general binomial of the form:

`(a-b)^(15)`

Will be expanded as follows using Pascal's triangle:

`a^(15)-15a^(14)b+105a^(13)b^2-455a^(12)b^3+1365a^(11)b^4-3003a^(10)b^5+5005a^9b^6-6435a^8b^7+6435a^7b^8-5005a^6b^9+3003a^5b^(10)-1365a^4b^(11)+455a^3b^(12)-105a^2b^(13)+15ab^(14)-b^(15)`

Now, from this we can see that the 11th term is given by:

`3003a^5b^(10)`

Now, in our case a = 3x and b = 2y, thus:

`\begin{gathered} 3003(3x)^5(2y)^(10)=3003(243x^5)(1024y^(10)) \\ \\ =747242496a^5b^(10) \end{gathered}`

So, the 11th term is:

`747242496a^5b^(10)`