# Expanding more than 2 sets of brackets....

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Hi, I'm being incredably dense at the moment, it's been about 5 years since I last thought about algebra and now the simplest thing is throwing me off... Ok, I'm trying to expand an equation with more than 2 sets of brackets... e.g. (x + 4) ^ 3 Step one I write out the power thing in full... (x + 4)(x + 4)(x + 4) Now what? I can try multiplaying everything by everything in one go (x*x*x, x*x*4, x*4*4, x*4*x, etc...) but I get the feeling the way to do it is to expand 2 of the sets of brackets then the result with the 3rd set of brackets, like so... (x + 4)(x + 4) = (x * x) + (x * 4) + (4 * x) + (4 * 4) = x^2 + 8x + 16 So far so good, now I've got... (x^2 + 8x + 16)(x + 4) This is where I get stuck, for some reason I think I fall foul here, I'd come up with the following... x^2 * x = x^3 x^2 * 4 = 4x^2 8x * x = 8x^2 8x * 4 = 36x 16 * x = 16x 16 * 4 = 64 there for I get... My ans = x^3 + 12x^2 + 48x + 64 Now this could be correct because I've just may up the values off the top of my dome but I fear it's not, I think I may have messed up somewhere (this conclusion is because I've got a similar exercise which I used the same method and got wrong). Can anyone either comfirm my workings or explain where I'm going wrong??? Would me much appriciated... I know this may look like a homework question but it's not...if I were still at school I'd remember how to do this :D

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(x+4)(x+4)(x+4) =
x(x+4)(x+4) + 4(x+4)(x+4) =
x2(x+4) + x4(x+4) + 4x(x+4) + 42(x+4) =
x3 + 4x2 + 4x2+42x + ...

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Ahh yeah, that works better :D Many thanks for that very, very speedy reply.

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Remember the Binomial Coefficients and theorem ?

The wiki explains it in very much detail. You will be interested in (x+y)^n, which is equation (2).

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