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# National 5 Multiplying out the brackets and simplifying question watch

1. Hi there,

I'm revising for my prelim and I came across this question in my text book and I just can't get the answer the text book is giving.

I need to multiply out the brackets and then simplify it.

(n+1)^3

The "^3" means the brackets are cubed.

The answer from the text book is:
n^3 + 3n^2 + 3n + 1

How do I get this answer?

Many thanks,
2. The simplest way would be to write out the expression in full:

(n+1)(n+1)(n+1)

3. (Original post by Actaeon)
The simplest way would be to write out the expression in full:

(n+1)(n+1)(n+1)

Okay. So then I would have:
(n+1) and n^2 + 2n + 1^2 ??

What next?
Could you be so kind and type out the working you would do?? It would help me a bit more.

Thanks,
4. (Original post by pianoforte123)
Okay. So then I would have:
(n+1) and n^2 + 2n + 1^2 ??

What next?
Could you be so kind and type out the working you would do?? It would help me a bit more.

Thanks,
Well, whenever you multiply two polynomials (your expressions) together, what you are really doing is taking each term in your first expression, and multiplying it by the entire second expression, then adding everything together.

For example, (a+b)(c+d) is a(c+d) + b(c+d).

So (n+1)(n^2+2n+1) is really n(n^2+2n+1) + 1(n^2+2n+1).

From there, it should be straightforward.
5. (Original post by Actaeon)
Well, whenever you multiply two polynomials (your expressions) together, what you are really doing is taking each term in your first expression, and multiplying it by the entire second expression, then adding everything together.

For example, (a+b)(c+d) is a(c+d) + b(c+d).

So (n+1)(n^2+2n+1) is really n(n^2+2n+1) + 1(n^2+2n+1).

From there, it should be straightforward.

Okay, so I did this n(n^2+2n+1) + 1
, and I got:
n^3 + 3n^2 + 1n + 1

I'm nearly there, just one more step to get that last part into 3n?

Thanks for helping me!
6. (Original post by pianoforte123)
Okay, so I did this n(n^2+2n+1) + 1
, and I got:
n^3 + 3n^2 + 1n + 1

I'm nearly there, just one more step to get that last part into 3n?

Thanks for helping me!
Where is that 3n^2 from

Where did the final bracket go

From n(n^2+2n+1) you should get a n-term of 1n (n by 1).
From 1(n^2+2n+1) you should get a n-term of 2n (1 by 2n).

Add them together and you get 3n.
8. (Original post by Actaeon)

From n(n^2+2n+1) you should get a n-term of 1n (n by 1).
From 1(n^2+2n+1) you should get a n-term of 2n (1 by 2n).

Add them together and you get 3n.
Oh right. Yup I got it now. Makes total sense.
Thanks again!

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