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    I've never understood binomial expansion in IGCSE and I certainly don't now. Is there any easy way to.. well.. make sense of it? I don't even get its purpose. Any easy ways to figure it out?

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    It's purpose is to work out expressions raised to a large power. For example (x+y) raised to the power of 10,000 lets say. You cannot sit at a table for weeks doing it. So they found a simpler way of doing it. Simplifying things is a lot of what maths is about.
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    Thank you!

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    The best way to learn if you don't understand is to figure it out yourself sometimes- if you cannot, then research. Anyway- I will post an explanation here, anyway, it will serve as practising LaTex. Please bare with me and come back later in the day.
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    Ever heard of pascals triangle? This is basically what I will show you with a basic example and explanation. {This isn't an answer to any questions and is identical to the explanations on external sources- so op's please don't ban me/ remove this as it also took a long time to make }
    Binomial expansions exist as expanding expressions raised to a large power (lets say above 5'ish) is tricky, tedious and time consuming. So why bother when some wonderful mathematicians created such a simple and quick way of doing it?
      So.......... (x+1)^2= x^2 +2x+1
    With the terms multiplied by x in this direction..) \swarrow

    Makes (x+1)^3= x^3 +3x^2 +3x+1
    As you can see the x^2 turns into x^3 by a multiplication of x. So, all the terms are multiplied by x, so all terms of x are raised by one degree (the indice raised by 1).

    ..So the 2x, for example is multiplied by x to make 2x^2. But wait... this is not equal the 3x^2 we seem to derive by multiplying by x. It's (obviously) because we are multiplying by x+1, not just x. So, by multiplying by 1, you are just adding the original term onto the multiplied term.
    So, we derive 2x^2 by multiplying the  2x,by,x , but this is then added by the x^2 in the original expression [as we do as it's multiplied by (x+1)] to make 3x^2.. So as you can see it's very much like Pascals Triangle, which is just a more simplified version of sed explained concept, in which the two numbers above the new number add to create the new number. So, you can see with the example that I used that, like in Pascals Triangle, the x's at the side remain the same, (coefficient wise) , just raised to a higher power each time. So to summarise, the expression is multiplied by x, then the original expression is added to it. So you can surely see that it's like the triangle,
    We then find, that by expanding expressions multiple times, the terms are raised to a higher power each time and the original expression is added on to it, which creates a pattern, ...and these coefficients then make the pattern of pascals triangle. So, look at the expressions (near the arrow) above and if you don't understand try to make sense of it or just take it.
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    (Original post by nafisa.t13)
    I've never understood binomial expansion in IGCSE and I certainly don't now. Is there any easy way to.. well.. make sense of it? I don't even get its purpose. Any easy ways to figure it out?
    What part are you unsure of?

    Is it how to find the coefficients - are you asking for help understanding how the nCr works?
 
 
 
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