Binomial Expansions Reflection Sadie 8A

Level 1-2

•If you were an engineer 100 years ago, explain how our method may have been useful rather then just using long multiplication?

•Using this method is more useful then using long multiplication because by using this method you are able to write everything out and see what you are working with. From there you can simplify. Also the more decimals points the harder it is to figure out.

ExampleOur Method(0.99)^2 = (1-0.01)(1-0.01)= 1(1-0.01)-0.01(1-0.01)= 1x1-1x0.01-

0.01x1+0.01x0.01= 1-0.01-00.01+0.0001= 0.9801

Level 3-4

•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?)

•If you get fairly long numbers or when you have many decimal places to work with you may want to just use long multiplication because then you won’t have to be constantly working things out and you can use just one simply equation.

Example

(93.22)^2= (100-6.78)(100-6.22)=100(100-6.22)-6.78(100-6.22)=100x100-100x6.78-6.78-100+6.78x6.78=10,000-678-678+45.96=8689.96

Level 5-6

•Can you give us some detailed explanations and examples of where long multiplication is more efficient than our expansion method?

•Long multiplication would be more useful when you have numbers that will take forever to figure out and expand and then simplify.

ExampleOur method:(136)^2=(100+36)(100+36)=100(100+36)+36(100+36)=100x100+100x36+36x100+36+

36=10,000+3,600+3,600+1,269=18,469(Not to mention they wouldn’t have a calculator to help figure it

out)

Benefits Of Our Method

•Using this method you are able to see everything your working with and its more step by step.

•This method is neater and more organized.

•For some equations its difficult to use long division so to be able to expand the equation and then simplify it makes it easier to answer.

Limitations of Our Method

•Using this method you will end up writing so much out, and it will end up being a longer equation. Therefore it makes it easier to make mistakes.

•When using this method you might use it so often that when it comes to using long multiplication you will struggle because this method is only useful sometimes.

•When you use this method you have to round to the nearest 10th or 100th.