# Binomial expansion- have I done this correctly?

• February 28th 2010, 06:06 AM
fishkeeper
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?

Quote:

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

$(2 + x) (1 + x)^5$
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 :D

Ok:

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

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

2) Multiply by first bracket:

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

Equals: $(2+x) + (10x+5x^2) + (20x^2+10x^3) + (20x^3+10x^4) + (10x^4+5x^5) + (10x^5+x^6)$
Note: put in brackets to make it easier to read.

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

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

I got the above answer, however the book's answers got $2+ 11x + 25x^2$ and I cannot find the extra $x$ 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 $!$and $nCr$ button on my calculator?

Thankyou very much!
• February 28th 2010, 06:41 AM
skeeter
Quote:

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 :D

Ok:

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

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

2) Multiply by first bracket:

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

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

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

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

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

I got the above answer, however the book's answers got $2+ 11x + 25x^2$ and I cannot find the extra $x$ 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 $!$and $nCr$ button on my calculator?

Thankyou very much!

see the 11x now?
• February 28th 2010, 06:44 AM
fishkeeper
Quote:

Originally Posted by skeeter
see the 11x now?

Haha thanks

Was my method alright though?

thanks again!