1. ## binomial expanding

I'm supposed to use the Binomial Theorem to simplify the two following problems

and...

But I'm completely stumped, I have absolutely no idea how to use the binomial theorem and am in need of some step by step help. I'd appreciate it tremendously.

2. Originally Posted by Samurai Karasu
I'm supposed to use the Binomial Theorem to simplify the two following problems

The binomial theorem states

$(a+b)^n=\sum_{k=0}^{n}\binom{n}{k}(a)^{n-k}(b)^k$

so we we identify the parts a=x b=(-2) and n=4

$(x-2)^4=\sum_{k=0}^{4}\binom{4}{k}(x)^{4-k}(-2)^k$

Now we let k=0,1,2,3,4

$\sum_{k=0}^{4}\binom{4}{k}(x)^{4-k}(-2)^k=\binom{4}{0}(x)^{4-0}(-2)^0+\binom{4}{1}(x)^{4-1}(-2)^1$
$+\binom{4}{2}(x)^{4-2}(-2)^2+\binom{4}{3}(x)^{4-3}(-2)^3+\binom{4}{4}(x)^{4-4}(-2)^4=$

$x^4-8x^3+24x^2-32x+16$

See what you can do with the next one.

3. I seriously just got it!

The only thing I had to think about was you need to use Pascal's Triangle to put coefficents in front of the numbers, but otherwise I finally got it! Thank you tremendously my man, I think I might be able to do good on that test tomorrow thanks to you.