Expand in terms of binomials coefficients

I am asked to expand and simply the following expression.

(x + √2)7 + (x - √2)7

I have my notes here on the binomial theorem, and it seems simply enough to expand each of those terms.....except.

In my notes it says

(x+y)^n= then goes on the expand here with each term added to the next.

It does not mention anything about...

(x-y)^n ?

Is it the same as addition except each term is subtracted from the next?

Re: Expand in terms of binomials coefficients

Quote:

Originally Posted by

**ehpoc** It does not mention anything about...

(x-y)^n ?

Is it the same as addition except each term is subtracted from the next?

$\displaystyle \left( {x - y} \right)^n = \sum\limits_{k = 0}^n {\binom{n}{k}\left( x \right)^{n - k} \left( { - y} \right)^k } $

Note that in your question, odd powers subtract out.

Re: Expand in terms of binomials coefficients

SO basically when all is said and done the two expansions will look the same but with negative signs where the positive signs are?

Ok so when I expanded the two terms

One had eight positive terms.

The other had same terms but negative except for the very first term than contained no y.

So once I cancelled out I got.....2x^7

Re: Expand in terms of binomials coefficients

Quote:

Originally Posted by

**ehpoc** SO basically when all is said and done the two expansions will look the same but with negative signs where the positive signs are?

Well you missed it answer.

Look at this.

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Re: Expand in terms of binomials coefficients

What!!?!?!?!

How did that happen?