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January 9th, 2016, 07:23 AM   #1
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(Binomial Expansion) Could someone please help me?

I have an exam next week and I have been practising some questions.
Could anyone please give me the answers to the following questions?

I was only able to do 6(a) and parts of 7.
Would be really helpful.
Thanks in advance.

Last edited by skipjack; January 9th, 2016 at 07:45 AM.
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January 9th, 2016, 07:50 AM   #2
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Below are some hints or partial answers.

5. The expansion is $\displaystyle 2^6 + 6\left(2^5\right)Ax + 15\left(2^4\right)A^2x^2 + \,...$, so compare that to $64 - 576x + Bx^2$.

6.(a) $\displaystyle (1 - x)^7 = 1 - 7x + 21x^2 - 35x^3 + 35x^4 - \,...$
6.(b) Use $x$ = 0.01 in the above. The last term shouldn't be needed.

7. $\displaystyle (1 + 4x)^4 = 1 + 16x + 96x^2 + 256x^3 + 256x^4$ and $\displaystyle (1 - 2x)^6 = 1 - 12x + 60x^2 - 160x^3 + 240x^4 - 192x^5 + 64x^6$.

8. Does $\displaystyle (1 + 2x)^n = 1 + 2nx + 2n(n - 1)x^2 + \,...$ help you?

If you need further help, can you post what you were able to do, given the above?
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January 9th, 2016, 09:48 AM   #3
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5. I got as far as this:

I failed to be able to find the values for a and b, I was completely stuck.
6. I was able to to this question, the answer that I got for b is:

7.
I'm not sure if that's right, seems way too little for a 6 mark question.
EDIT: I am now able to do it thanks to a friend who explained it to me.
8. completely confused, dont know where to even start
@skipjack
Thanks for the help in advance

Last edited by skipjack; January 9th, 2016 at 12:30 PM.
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January 9th, 2016, 01:04 PM   #4
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EDIT:
I am able to do all questions except 5
I got n=7 for number 8 if that's right

Last edited by nautudent; January 9th, 2016 at 01:10 PM.
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January 9th, 2016, 01:07 PM   #5
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5. You got (Ax)², but changed it to Ax² instead of A²x². The next step should be to make the comparison I suggested.

As 192A = -576, A = -576/192 = -3, and so B = 240A = -720.

6. You got the correct value. Do you see why only the first half of the complete expansion is needed?

7. The product includes (16x)(-12x) = -192x², so the answer is 156 - 192 = -36.

8. The coefficient of x² is six times the coefficient of x, so 2n(n - 1) = 6(2n), i.e. 2n² - 2n = 12n.
Dividing by n (which is not zero) gives 2n - 2 = 12, so n = 7.
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