A level Maths - Binomial Expansion

Brian is no good at maths · 2011-02-01 04:29:15

Hey Stuck on some home work questions and wondered if some nice person would lend a hand?

The 2 questions are as follows:

The expansion of (2-px)^6 in ascending powers of x, as far as the term in x^2, is
64+Ax+135x^2
Given that p > 0, find the value or p and the value of A

[7 marks]

And number 2:

The first four terms, in ascending powers of x, of the binomial expansion of (1+kx)^n are
1+Ax+Bx^2+Bx^3+....,
Where k is a positive constant and A,B and n are positive integers.

(a) By considering the coefficients of x^2 and x^3, show that 3 = (n-2)k

[4 marks]

(b) Given that A = 4, find the value of n and the value of k.

[4 marks]

Any help would be greatfully received
Cheers for your Help Bry

gAr · 2011-02-01 04:55:02

Hi,

It's easy if you know binomial expansion.

For Q1)
the expansion: p^6*x^6 - 12*p^5*x^5 + 60*p^4*x^4 - 160*p^3*x^3 + 240*p^2*x^2 - 192*p*x + 64
Next you equate the co-efficients:
for x^2,
240*p^2 = 135
therefore, p = 3/4

for x,
A = -192*p = -144

Try the second question similarly, math is fun, you must learn!

Last edited by gAr (2011-02-01 05:03:36)

Brian is no good at maths · 2011-02-01 07:07:08

I dont under stand where you get some of the numbers from??? :S may just be me being a ****. Couldnt go into more detail could you? :S

Bob · 2011-02-01 07:22:29

Hi Brian

It is 19.21 GMT. Are you logged on at the moment? If yes, please reply and we'll have a 'talk' about your questions.

Bob

Brian is no good at maths · 2011-02-01 07:25:42

Hi, Yes I am, Just trying to do my PE home work at the moment!

How do you propose to have a chat?

Cheers for the response Bry

Bob · 2011-02-01 07:27:33

hi Bry,

Good to 'hear' from you. This is the 'chat'.

Is your PE hw to roll about on the floor laughing?

Let's start with question 1. Have you understood how to do it?

Bob

Last edited by Bob (2011-02-01 07:28:44)

Brian is no good at maths · 2011-02-01 07:31:46

Unfortunately.... No its not

Well I under stand what i have to find (after all it does tell me what it wants) But I took one look at this question and was like *oh dear!* and how the guy before explained it before confuzzed me some more!!!

Bob · 2011-02-01 07:36:38

hi Bry,

That's what I was wondering.

Ok, have you 'done' the binomial theorem. That's the one with things like

or maybe you used Pascal's triangle?

Bob

Brian is no good at maths · 2011-02-01 07:41:38

We have be taught to use pascals triangle as you can work that out on your calculator (calculators are my friends )

Bob · 2011-02-01 07:49:17

Great.

So for power 6 you want

1 6 15 20 15 6 1

and then the terms are

I stopped at x squared because the question does too. (just corrected an error there. whoops)

Ok so far?

Bob

Last edited by Bob (2011-02-01 07:55:37)

Brian is no good at maths · 2011-02-01 07:59:02

Yep, I get that

Bob · 2011-02-01 08:09:27

Excellent!

So now we can put those terms equal to the ones given in the question.

Well. The first tells me something I already knew. Nice to have it confirmed that 2x2x2x2x2x2=64 but not much help with the problem.

The second has two unknowns, A and p so I'll leave that for the moment.

But

I can do something with.

Don't forget a minus times a minus is plus.

Get rid of the x^2 and we have

Time for your calculator I think as I haven't got one nearby.

So what do you make p?

Bob

Last edited by Bob (2011-02-01 08:10:26)

Brian is no good at maths · 2011-02-01 08:21:49

I make it 3/4.... Which is what the other guy got

MathsIsFun · 2011-02-01 08:32:43

Also read: http://www.mathsisfun.com/algebra/binomial-theorem.html

Bob · 2011-02-01 08:33:43

He sure did. So I think we'll take that as correct!

Now on to question 2.

As you don't yet know 'n' you cannot just write out the rows of Pascal's triangle. And your calc. won't be able to either because it'll want to know the value of n.

Luckily, there's a way of calculating the numbers for any row without having to know the ones before.

For the nth row it is:

The third and fourth terms both have coefficient B so we can put them equal

Most of that cancels out so over to you again. Simplify as much as you can. What are you left with?

Bob

Last edited by Bob (2011-02-01 09:47:35)

Brian is no good at maths · 2011-02-01 08:45:03

n(n-2)
---------- kx ?????? Have i done that right? :S
3

Bob · 2011-02-01 08:50:48

Very close but not quite. You seem to have lost the equals sign.

Do some cancelling eg k squared

becomes

Please try again.

Bob

Last edited by Bob (2011-02-01 09:50:16)

Brian is no good at maths · 2011-02-01 08:59:09

Does this mean I have to expand the n(n-1) on the left to put it over the other side?? :S

Bob · 2011-02-01 09:10:52

No need. Look on the left for something that is also on the right. If found cancel them to make a simpler equation.

eg k squared will go.

Bob

Brian is no good at maths · 2011-02-01 09:11:03

Really sorry but I have to go

Thanks for all your help really appreciate it I think I may have to make a trip to one of my maths teachers tomorrow and get them to explain it Maths is okay.... Its just the teachers :L

Thanks again!!!!!!!!!!!!!!!! Cheers Bry

Bob · 2011-02-01 09:17:26

Ok bye.

I suggest you sign up to Maths is Fun because then you get emails on your topics and can see who is on-line.

Good luck

Bob

Math Is Fun Forum

#1 2011-02-01 04:29:15

A level Maths - Binomial Expansion

#2 2011-02-01 04:55:02

Re: A level Maths - Binomial Expansion

#3 2011-02-01 07:07:08

Re: A level Maths - Binomial Expansion

#4 2011-02-01 07:22:29

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#5 2011-02-01 07:25:42

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#6 2011-02-01 07:27:33

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#7 2011-02-01 07:31:46

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#8 2011-02-01 07:36:38

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#21 2011-02-01 09:17:26

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