Binomial Expansions Reflection

1. Binomial ExpansionsReflection By: Ali Al Naema

2. If you were an engineer 100 years ago, explain how our method may have been useful rather than just using long multiplication The method we used is real useful than the long multiplication because it saves time and it makes it easy to solve hard numbers, it also is easy because if your in a rush these days you can just use a calculator but in the old days it takes time and engineers don’t have much time. Example: (1100)² = (1000+100)(1000+100) = 1000² + 2 x 1000 x 100 + 100² It is easier then doing it in long multiplication

3. At what point would our method be big and cumbersome? (ie. How many decimal places or what sorts of numbers would make us think twice about using this method?) For me I think that I will think twice about using the method if it is to three decimal places or if they are long numbers not 1000 or 100 I mean 544 or 2676 it is much easier doing it in any other way than using the method. Example: If I had 544 I would do it long multiplication then using the method. 544 X 544 __________ 2176 21760 272000 ___________ 295939

4. Can you give us some detailed explanation and examples of where long multiplication is more efficient than our expansion method? Although our expansion method is very useful and better than long multiplication, sometimes the long multiplication is more efficient then our method because sometimes there are things that don’t need the use of methods. Example: 5² = (2+3)(2+3) =2² + 2x2x3 + 3² =4+12+9 = 25 5²= 5 x5 ______ 25

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