Thread: Binomial expansion- have I done this correctly?

1. Binomial expansion- have I done this correctly?

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?

Expand the following in ascending powers of $\displaystyle x$ up to and including the term $\displaystyle x^2$

$\displaystyle (2 + x) (1 + x)^5$
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: $\displaystyle (2+x) + (10x+5x^2) + (20x^2+10x^3) + (20x^3+10x^4) + (10x^4+5x^5) + (10x^5+x^6)$
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!

2. Originally Posted by fishkeeper
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!
see the 11x now?

3. Originally Posted by skeeter
see the 11x now?
Haha thanks

Was my method alright though?

thanks again!