Binomial Expansions- Reflection

1. Binomial Expansions- Reflection By: Abdullah Al-Hendi

2. Main Question? The main questions was is there a simple way to do 0.992? A discovery proofed that we can do this using binomial expansion 0.992 = (1-0.01) (1-0.01) = 12-2x1-0.01+(-0.01) (-0.01) = 0.9801

3. Method For the square of the sum of two number: (a+b)2 = a2 + 2ab + b2 the first term squared, added by the product of the 1st and 2nd term multiplied by two, plus the last term squared.

4. Method part 2 For the square of the difference of two numbers: (a-b)2 = a2 - 2ab + b2 the first term is squared, the product of the 1st and 2nd term squared is then subtracted from the 1st term squared, added by the last term squared

5. Engineers 100 years ago It would have been very helpful to engineers 100 years ago. The answer would have been most likely to be right for equations they needed for structures and such. It is much quicker to answer. More reliable.

6. Thinking Twice This method is efficient but not perfect. 1) Big numbers, reaching the digits of thousands, or millions, and so on is very difficult to answer. 2) A large amount of decimals will also increase its difficulty. 3) Also when the number is cubed or to the power of 4, etc. Example: 3.7461726 squared, 7591726 squared, or 3267 to the power of 4

7. Long Multiplication? Long multiplication could be more efficient at times. When the number itself is too long. When the amount of decimals is very long. When the number is cubed, or to the power of 4, power of 5, etc. Examples: 3.7461726 squared, 7591726 squared, or 3267 to the power of 4

8. Long Multiplication part 2 Long Multiplication Binomial Expansion 992 = (100-1)2 = 10000 – 2x100x1 + 1 = 9801 992= 899 x99 891 +8910 9801

9. Conclusion Binomial expansion is very useful for number with the digits of 3 and less. However, it is very difficult to use it with long decimals, and numbers with digits 4 and more. In some cases long multiplication will be needed.