AS Maths binomials??

  • 0 votes

I am really confused this binomial  question and was wondering if anyone knew how to solve it? Thank you!

If x is so small that x (cubed) and higher powers are negligable show that

(3x - 2x) (1+2x)^10 (squiggly equals sign;))  3 +56x+500x^2

Posted Wed 24th October, 2012 @ 19:01 by AmyPond

3 Answers

  • 2 votes

I could be COMPLETELY wrong but this is what I did and my answer sort of resembles the question.

So, if powers of 3 and higher are negligible then when we expand the binomial, we are only interested in the first 3 terms of 1, x and x^2.

So when we do expand it, we get the first three terms to be 1 + 20x +180x^2

Then if we multiply this by (2x-3) (btw I tried it with 3x-2x which would then just be x and I tried it with 3x-2 which doesn't work either, so I resulted to 2x-3 :)

So anyways, if we multiply the two brackets (1+20x+180x^2)(2x-3) we get:

3+ 60x- 2x + 540x^2 - 40x^2 -360x^3

Since powers of 3 or more are negligible I ignored the 360x^3 and then collected the remaining like terms together.

So then it came out to 3+58x+500x^2!!

I realise that I did a bit of manipulating and I got 58x and not 56x but it's the closest I could get. 

When you find out the actual answer please let me know, I NEED to know.

Hope that somewhat helped, but I highly doubt it 

^_^ x

Answered Thu 25th October, 2012 @ 21:03 by Nuha
  • 1 vote

Thank you!:) used this as a base and went to my Maths teacher:) he said that the negligible bit was right but you multiply put the brackets with 3-2x:) but the 56x was a typo and you do actually get 58x at the end!:) so you were right:)

Answered Fri 26th October, 2012 @ 07:11 by AmyPond
  • 0 votes

Yay! That's great to hear :)

Good luck with the rest of your year!

Answered Sat 27th October, 2012 @ 13:07 by Nuha