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# Help with Binomial Expansion question.

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1. Hi, I did this a few weeks ago, but now I have come back to it I feel I am doing the right thing but I am getting the wrong answer everytime I try it.

Expand (1 + x + x²)^3 as far as the x^3 term.

I did this: [ 1 + (x + x²)]^3

= 1 + [x^3] + [3x²(x²)] + [3x(x²)²] + (x²)^3

And when I simplify this (excluding the terms with powers greater than 3), I get the wrong answer. Have I done something wrong or is the answer wrong? I would give you the answer so you can tell me if its right, but my book isn't currently with me, sorry.
2. (Original post by ERdoctor)
Hi, I did this a few weeks ago, but now I have come back to it I feel I am doing the right thing but I am getting the wrong answer everytime I try it.

Expand (1 + x + x²)^3 as far as the x^3 term.

I did this: [ 1 + (x + x²)]^3

= 1 + [x^3] + [3x²(x²)] + [3x(x²)²] + (x²)^3

And when I simplify this (excluding the terms with powers greater than 3), I get the wrong answer. Have I done something wrong or is the answer wrong? I would give you the answer so you can tell me if its right, but my book isn't currently with me, sorry.
Where did you use binomial expansion here?
3. SORRY!

I think I know what i did wrong. I should have factorised the (x + x²)^3 bracket to get a 1 for the first term, other wise the expansion won't work. My mistake!

Am I right?
4. Have you multiplied the terms by the binomial coefficients as well? You know, the ones you get off Pascal's triangle?
5. (Original post by raheem94)
Where did you use binomial expansion here?
I didn't show my full working out, but I did use binomial expansion. I think I know where I got it wrong though, I should have factorised more and got a 1 as my first term instead of X.

So rather than having [1 + (x + x²)]^3

I would have [1 + x(1 + x)]^3 Before expanding binomially.

Is that right?
6. (Original post by ERdoctor)
SORRY!

I think I know what i did wrong. I should have factorised the (x + x²)^3 bracket to get a 1 for the first term, other wise the expansion won't work. My mistake!

Am I right?
Just use the formula,

Where n=3 and x=(x+x^2)
7. Ahhh, so you do two separate binomial expansions, and then add their x^3 terms together... I think that could work.
8. (Original post by ERdoctor)
I didn't show my full working out, but I did use binomial expansion. I think I know where I got it wrong though, I should have factorised more and got a 1 as my first term instead of X.

So rather than having [1 + (x + x²)]^3

I would have [1 + x(1 + x)]^3 Before expanding binomially.

Is that right?
You should use, [1 + (x + x²)]^3, i have tried it and i get the right answer.

Spoiler:
Show

9. (Original post by raheem94)
Just use the formula,

Where n=3 and x=(x+x^2)
Yeah, that worked. I knew I was over complicating it again.

Thanks! My answer was 1 + 3x +6x² + 7x^3
10. (Original post by ERdoctor)
Yeah, that worked. I knew I was over complicating it again.

Thanks! My answer was 1 + 3x +6x² + 7x^3
Your answer is correct .

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Updated: February 29, 2012
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