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C1 Binomial Expansion Watch

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    I was wondering if anybody could give me a heads up on where to start with this question please!

    Find the coefficient of x^3in the expansion of (2 – 3x)^3(1 – x)^4
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    Holy crap what exam board are you doing?
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    (Original post by Babs Posh)
    I was wondering if anybody could give me a heads up on where to start with this question please!

    Find the coefficient of x^3in the expansion of (2 – 3x)^3(1 – x)^4
    What would you do if you just have one instead of one being multiplied by another?

    So is there anything you can do, knowing that?
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    (Original post by zayn008)
    Holy crap what exam board are you doing?
    OCR MEI but this isn't from a past paper, we're given harder questions for homework so the exam is somewhat 'easier'

    (Original post by SeanFM)
    What would you do if you just have one instead of one being multiplied by another?

    So is there anything you can do, knowing that?
    Well... only using (2-3x)^3 the coefficient of x^3 that I get is -216.

    I don't really know how to go about the second one My guess would be to perhaps expand it fully and see what makes x^3 but I'm really not sure haha!
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    (Original post by Babs Posh)
    OCR MEI but this isn't from a past paper, we're given harder questions for homework so the exam is somewhat 'easier'



    Well... only using (2-3x)^3 the coefficient of x^3 that I get is -216.

    I don't really know how to go about the second one My guess would be to perhaps expand it fully and see what makes x^3 but I'm really not sure haha!
    I'm doing MEI too and my teacher does the same, she gives us edexcel binomial expansion which is C2 for them, I could do this question if I had a calc but that would be cheating Name:  image.png
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    (Original post by Babs Posh)
    OCR MEI but this isn't from a past paper, we're given harder questions for homework so the exam is somewhat 'easier'



    Well... only using (2-3x)^3 the coefficient of x^3 that I get is -216.

    I don't really know how to go about the second one My guess would be to perhaps expand it fully and see what makes x^3 but I'm really not sure haha!
    You may want to check that - the coefficient of x^3 in the expansion of (2-3x)^3 isn't -216. You know it's (2-3x)(2-3x)(2-3x) and there's only one way to get an x^3 term (by multiplying -3x by -3x and by -3x, giving you... (that's not exactly how you do this question, it's just a handy way of checking that you've done it right).
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    (Original post by SeanFM)
    You may want to check that - the coefficient of x^3 in the expansion of (2-3x)^3 isn't -216. You know it's (2-3x)(2-3x)(2-3x) and there's only one way to get an x^3 term (by multiplying -3x by -3x and by -3x, giving you... (that's not exactly how you do this question, it's just a handy way of checking that you've done it right).
    Ah I see! I've noticed where I've gone wrong as well, I now get -27x^3 Do I now find the coefficient of x^3 in the second bracket and multiply?
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    (Original post by Babs Posh)
    Ah I see! I've noticed where I've gone wrong as well, I now get -27x^3 Do I now find the coefficient of x^3 in the second bracket and multiply?
    Afraid not, it's not as simple as that .

    In one expansion, eg (2-3x)^2 to keep it simple, there's only one way of getting x^0 (and that's by multiplying 2 by 2) and one way of getting x^2 (-3x by -3x), but to get x you can do -3x by 2 and -3x by 2 (which seems like the same thing but there are two of them, so that leaves you with -12x rather than -6x.

    Similarly, when you're multiplying (a + bx + cx^2 + dx^3....) (e + fx + gx^2 + hx^3)... there are multiple ways of getting to x^3. So you can either spot which ones are going to give you x^3 (which you can do after a bit of practice..) or expand everything but cross out anything that isn't x^3.
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    I recommend going through every question in the past papers, answer them and compare with the markscheme. The best way to make it stick!!

    Ahh, and you can find past papers on ocr's website, exam solutions, igcseworld.com, etc..
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    binomial expansion then match up all the terms that will times together to get you an x^3 like x^2 and x x^3 and an integer ect and add them all up
 
 
 
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