[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.

[raheem94]

(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?

[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?

[Lifeisgood:)]

Have you multiplied the terms by the binomial coefficients as well? You know, the ones you get off Pascal's triangle?

[ERdoctor]

(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?

[raheem94]

(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)

[Lifeisgood:)]

Ahhh, so you do two separate binomial expansions, and then add their x^3 terms together... I think that could work.

[raheem94]

(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

[ERdoctor]

(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

[raheem94]

(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 .