# Thread: Expanding with binomial theorem

1. ## Expanding with binomial theorem

Hi, I was working through some exercises and came to this:

$(x^2+y)^7$

I got an answer which starts out as:

$x^{14}+7x^{12}y+21x^{10}y^2$....

etc. etc.

$x^{14}+7x^{12}+21x^{10}y^2$.....

note the missing $y$ from the " $7x^{12}$" part.

This seems kooky to me, am I wrong or is the book wrong? And if I'm wrong, what did I do wrong?

2. You are correct. The book probably just has a typo.

3. Thanks for that, I was hoping it was a typo.

But I have a related question. I've continued in this exercise set and have another question about how to handle negatives, for example in the problem:

$(2x^2-y^2)^6$

The first time I expanded this, I got $(2x^2)^6 + 6(2x^2)^5 (-y^2) + 15(2x^2)^4 (-y^2)^2$.....etc.

but when I went to do the next step, I noticed that everything came out positive because of the $(-y^2)$ thing.

so I rewrote it as $(2x^2)^6 + 6(2x^2)^5 *-(y^2) + 15(2x^2)^4 *-(y^2)^2$.......etc.

This gives the right answer, but it looks messy, and I'm not happy with it because I just pulled it out of my ear, so to speak.

I guess my question is, Am I doing this correctly or should I go back and do some rereading?