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Binomial Expansion-Reflection

Binomial Expansion-Reflection. By Tamim El Moatassem 8B Math Mr. Korbatits. Introduction. In our investigation we looked at patterns in binomial expansions . we came to the general rule for expanding binomials, in particular squaring the sum and difference of two terms:

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Binomial Expansion-Reflection

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  1. Binomial Expansion-Reflection By Tamim El Moatassem 8B Math Mr. Korbatits

  2. Introduction In our investigation we looked at patterns in binomial expansions. we came to the general rule for expanding binomials, in particular squaring the sum and difference of two terms: (a+b)2=a2+2ab+b2 and (a-b)2=a2-2ab+b2

  3. Part 1 If you where an engineer over 100 years ago, explain how our method may have been useful rather than just using long multiplication? My answer is: it would be easier and more efficient because doing long multiplication would take you a while but here we can split the number up into two parts and square them. So if you have a number like 992 and you can break it up into (90+9)2 which would be much more efficient and quicker to do.

  4. Part 2 At what point would our method be big and cumbersome? My answer is : numbers having more than 4 or 5 places or with very high powers would be big and cumbersome . Because if you had 13242 then you cant split it up too well it would come out to be (1300+24)2 or (1320+4)2 and there are other outcomes that would still be difficult. Or for the high powers it would look like this for 16796 it would become (1600+79)6 and that isn't very easy when using binomial expansion.

  5. Part 3 Could you give us some detailed explanations and examples of where long multiplication is more efficient than our expansion method? Here are some examples: 89465=(8900+46)5 this would be hard to do because 8900 multiplied by 5 is not a simple problem to do neither is 46. so for this equation I would use multiplication. Because the multiplication would be one straight forward step which would be 8946x8946 etc although this would take more steps you are less likely to make mistakes. With the binomial expansion you have different signs and operations so you could make numerous mistakes between all of the steps. This is continued on the next slide.

  6. Part 3 continued 46813=(4700-19)3 this one is subtraction but would still be easier because you would have to multiply two different numbers three times but with long multiplication its just three straight multiplications like: 4681x4681=21911761x4681=102568953241x4681=4.80125269+14. this may look like a big and hard number but it would be even harder with binomial expansion.

  7. A2 Thank You For Watching

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