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Binomial Expansions- Reflection

Binomial Expansions- Reflection. By: AlJohara T. AlThani 8B. Introduction. How useful are binomial expansions, and are there times when it is better not to use them? This presentation will try to answer these questions. A binomial expansion is for example: (a+b) 2 =a 2 +2ab+b 2. Example.

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Binomial Expansions- Reflection

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  1. Binomial Expansions- Reflection By: AlJohara T. AlThani 8B

  2. Introduction How useful are binomial expansions, and are there times when it is better not to use them? This presentation will try to answer these questions. A binomial expansion is for example: (a+b)2=a2+2ab+b2

  3. Example 522= (50+2) (50+2) = 50x50+50x2+50x2+2x2 = 2500+100+100+4 = 2704

  4. 100 Years Ago… This could have been useful because it is a way to break down large numbers into smaller numbers, which can be multiplied mentally. So an engineer on a worksite could calculate this in his head.

  5. 100 Years Ago… Also, this method is a way of checking that long multiplication answers are correct. It is a second method so, if both answers are not the same, the engineer could double check both answers.

  6. Can We Always Use This Method? If the number has three decimal places or more, it is not easy to use this method if the number cannot be broken into smaller numbers that are easy to multiply mentally.

  7. Can We Always Use This Method? For example: 0.0152=(0.01+0.005)2. This can be done using the method, but, 0.3692=(0.36+0.009)2 OR (0.3)+0.069)2. Both of these are difficult to calculate mentally.

  8. Can We Always Use This Method? A second case is where the number is a whole number greater than 200 which cannot be broken into smaller numbers easy enough to multiply. If they are multiples of 10, then they could be broken into smaller numbers and multiplied

  9. Can We Always Use This Method? For example, 2202=(200+20)2 But, 2242=(200+24)2. The first is easy, but the second one is not.

  10. Long Multiplication vs. Expansion Method So large numbers that are multiples of ten can use the method but other large numbers may not be able to use it and it would be more efficient to use long multiplication.

  11. Long Multiplication vs. Expansion Method In general, numbers which cannot be multiplied easily, or which cannot be converted to numbers that can be multiplied and squared easily are better solved using long multiplication

  12. Conclusion In conclusion, some numbers can be easily solved by expanding binomials, yet others cannot be broken into smaller simpler numbers. For example; 5432=(500+43) (500+43) And 5.432=(5+0.43) (5+0.43) OR (6-0.57) (6-0.57) None of these binomials is easy to solve using the method given to us in the investigation.

  13. Conclusion However, 2302= (200+30) (200+30) =200x200+200x30x2+30x30 = 40,000+12,000+900 =52,900 And 0.882= (1-0.12) (1-0.12) =1x1-2x0.12+0.12x0.12 = 1-0.24+0.0144 = 0.76+0.0144 = 0.7744 Can.

  14. THANQ FOR WATCHING!

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