Having problems w/ "find the term containing x^4 in the expansion of (x^2-2y)^7"

[hello123]

Having problems w/ "find the term containing x^4 in the expansion of (x^2-2y)^7"

Hello guys. Im having problems with the following question.
Any help would be greatly appreciate it. Thanks

1) find the term containing x^4 in the expansion of (x^2-2y)^7

 

[Deleted member 4993]

Hello guys. Im having problems with the following question.
Any help would be greatly appreciate it. Thanks

1) find the term containing x^4 in the expansion of (x^2-2y)^7

What are your thoughts regarding the assignment?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/for

 

[HallsofIvy]

Hello guys. Im having problems with the following question.
Any help would be greatly appreciate it. Thanks

1) find the term containing x^4 in the expansion of (x^2-2y)^7

Start with the binomial theorem: \(\displaystyle (x+ y)^n= \sum_{i= 0}^n\begin{pmatrix}n \\ i\end{pmatrix}x^iy^{n-i}\).

In this problem, n= 7 and, since \(\displaystyle x^4= (x^2)^2\) i= 2, you have to replace "x" with \(\displaystyle x^2\) and "y" with 2y, so the term is \(\displaystyle \begin{pmatrix}7 \\ 2\end{pmatrix}(x^2)^2(2y)^5\).

 

[Steven G]

Hello guys. Im having problems with the following question.
Any help would be greatly appreciate it. Thanks

1) find the term containing x^4 in the expansion of (x^2-2y)^7

What have you tried? Where do you think you made a mistake? Do you know the binomial theorem? If you tell us where you are stuck then we can help.