Binomial Expansion, help please?
- Thread starter Kim
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Your book should have a formula. There isn't anything really "deep" in this topic. You pretty much just apply the formula.
For (a + b)<sup>n</sup>, the terms are given by [nCm] a<sup>n-m</sup> b<sup>m</sup>, where "nCm" means "n-choose-m", that factorial thing you learned about.
So, for (x + 2y)<sup>12</sup>, the term with y<sup>8</sup> is going to have "8" as the power on the "2y" and thus 12 - 8 = 4 as the power on the "x". Work backwards from this to figure out the binomial coefficient (the n-choose-m thing), and multiply everything out.
Don't be worried if you get something really big; that's how these problems usually work out.
Eliz.
P.S. I wouldn't be surprised -- and wouldn't be the least bit offended -- if you think the above looks about "as clear as mud". The notation for this topic is a bear. For worked examples, try this online lesson, which might make a little more sense.
For (a + b)<sup>n</sup>, the terms are given by [nCm] a<sup>n-m</sup> b<sup>m</sup>, where "nCm" means "n-choose-m", that factorial thing you learned about.
So, for (x + 2y)<sup>12</sup>, the term with y<sup>8</sup> is going to have "8" as the power on the "2y" and thus 12 - 8 = 4 as the power on the "x". Work backwards from this to figure out the binomial coefficient (the n-choose-m thing), and multiply everything out.
Don't be worried if you get something really big; that's how these problems usually work out.
Eliz.
P.S. I wouldn't be surprised -- and wouldn't be the least bit offended -- if you think the above looks about "as clear as mud". The notation for this topic is a bear. For worked examples, try this online lesson, which might make a little more sense.