Binomial Theorem

Hydroex · 2010-06-26 02:03:15

Hello All, here it goes

(i)Write down the expansion of (1-x)^4

(ii)Use your result in (i) to show that the expansion of (1 - x + 2x^2)^4 in ascending powers of x up to the term in x^2 is given as 1 - 4x + 14x^2.

bobbym · 2010-06-26 02:22:07

Hi;

(i)

You can use the formula:

with x = - x and y = 1

Simplest is with pascals triangle for ( x + 1 )^n:

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1

So (1-x)^4 = x^4 - 4x^3 + 6x^2 -4x + 1

For (ii) you use:

( 2x^2 - x + 1)^4, just say a = 2x^2 - x and b = 1 in ( a + b )^4. You can now use the 5th row of pascals triangle. The idea is a little tricky but try to work it out yourself. If you need help, I will show you what I did.

Hydroex · 2010-06-26 03:18:29

Hm, i never really used pascals triangle before, but i will read up on it and give it a go. See how it goes then

bobbym · 2010-06-26 03:23:27

Once you have a handle on it. Take a look here for some harder ones.

http://ptri1.tripod.com/

Hydroex · 2010-06-26 04:29:03

Wow, just like a world of fantasy..

bobbym · 2010-06-26 08:29:48

Hi Hydroex;

Did you get the answer to ii ?

Math Is Fun Forum

#1 2010-06-26 02:03:15

Binomial Theorem

#2 2010-06-26 02:22:07

Re: Binomial Theorem

#3 2010-06-26 03:18:29

Re: Binomial Theorem

#4 2010-06-26 03:23:27

Re: Binomial Theorem

#5 2010-06-26 04:29:03

Re: Binomial Theorem

#6 2010-06-26 08:29:48

Re: Binomial Theorem

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