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Binomial Expressions

Binomial Expressions. By Shanthanu 8D Math. This is A fully automatic slide show please don’t click the computer will handle it. There Might be a 5-10sec delay due to animations. If you were an engineer 100 years ago, explain how our method may have been useful rather than long multiplication?.

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Binomial Expressions

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  1. Binomial Expressions By Shanthanu 8D Math This is A fully automatic slide show please don’t click the computer will handle it There Might be a 5-10sec delay due to animations

  2. If you were an engineer 100 years ago, explain how our method may have been useful rather than long multiplication? -It would be more useful in many ways but mostly it would save time. It would also be easier because we round it to 10 such as 742 we could just do (70+4) (70+4)=4900+280+280+16 which equals 5476 -Since we are rounding to the nearest tens place it is easier for us to calculate because 100 years ago they didn’t have calculators -If we did long multiplication it would have been 742=(74) (74) and to do 74*74 in your mind it would be hard because in the example above we can do it faster because multiplying by tens is easier. The answer would still be 5476 -The engineer would have a lot better time if he used our method it would be faster, easier, and simpler; he could still use long multiplication but it would save a lot more of his time

  3. At what point would this method be big cumbersome? (i.e. How many decimal places or what sort of numbers would make us think before using this method? • This method would start to get complex when we start moving out of the squared2and start going into the cubed3 then the 4th power4. Here is an example 244 would be (24+4)(24+4) (24+4) (24+4) which would be quite hard to do we would be better off if we just did this  • But if we are doing shorter numbers such • Such as squared or cubed it • It would be easier we use our method • But if we do long ones such as power 4 we are better of doing long multiplication in the end the answer is the same but the time taken and thoughts put in are different

  4. Can you give us some detailed explanations and examples of where long multiplication is more efficient than our expansion method • Long multiplications is more useful when there is a large number of digits or when the power is more then 3. • Our method called Binomial Expansions is more useful when we are dealing with small numbers and with numbers with low powers. • Here is an example where long multiplication is more useful “244” to do this with our method it would be (20+4) (20+4) (20+4) (20+4)=400+400+400+80+80+80+400+16+16+400+80+16= 331776 this took me about 5 minutes to solve but if we simply did  It would have taken us about one minute and it Would have been a lot simpler

  5. Conclusion/ One world • If I was a engineer 100 years ago I would stick to our method when it involves smaller numbers when it comes to large number we could use our method but it would me a bit hard to add such large digits without a calculator if we use long multiplication we could do it all in 2 steps • In the real world long multiplication is very good. Most contractors and engineers are paid per hour so this will save the contractors or builders some money; in short term their might be a $1000 but in long term the results can save up to $100,000

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