We have only been taught how to do single bracket expansions, so this is my first bracket one, so please can you tell me if Ive done anything wrong?

P.S I dont know how to use the factorial method so Im using pascal's triangle. If anyone has any helpful points on the factorial method, please tell me

Ok:

1) $\displaystyle 1(1)^5 + 5(1)^4(x)1 + 10(1)^3(x)^2 + 10(1)^2(x)^3 + 5(1)^1(x)^4 + 1(x)^5$

Equals: $\displaystyle 1 + 5x + 10x^2 + 10x^3 + 5x^4 + x^5$

2) Multiply by first bracket:

$\displaystyle (2+x)(1) + (2+x)(5x) + (2+x)(10x^2) + (2+x)(10x^3) + (2+x)(5x^4) + (2+x))x^5)$

Equals: $\displaystyle (2+\textcolor{red}{x}) + (\textcolor{red}{10x}+5x^2) + (20x^2+10x^3) + (20x^3+10x^4) + (10x^4+5x^5) + (10x^5+x^6)$

Note: put in brackets to make it easier to read.

3) Put in order up to $\displaystyle x^2$

$\displaystyle 2 + 10x + 25x^2$....

I got the above answer, however the book's answers got $\displaystyle 2+ 11x + 25x^2$ and I cannot find the extra $\displaystyle x$ that I am missing

I am guessing the method that I used is correct or not? and how would this question be done using the $\displaystyle ! $and $\displaystyle nCr$ button on my calculator?

Thankyou very much!