3. Use of our Method in Engineering Long Ago A hundred years ago the calculation of big numbers was extremely difficult because not many methods were developed. People didn’t have calculators but instead everything was done with pencil and paper. For engineers it was particularly hard because they needed to take a lot of measurements and a lot of multiplication took place. The method that we came up with would have helped them a lot because in some cases engineers would have had to at some point multiply big numbers in order to figure out the area of something and with long multiplication some mistakes could occur which could lead to a lot of problems when it comes to building a house or or anything because if the measurements are not correct than the building will be out of proportion. If our method was used then engineers wouldn’t have had to multiply a lot of big numbers together which means that the amount of errors possible would decrease resulting in completing the measurements faster and creating good buildings.

5. This is 980 2 using the method we came up with: (980) 2 = ( 900+80) (900+80) = 900 2 + 2(80 x 900) + 80 2 = 810000 +144000 + 6400 = 960, 400 Now we were able to use binomial expansion for this question even though the number was pretty big because it is even so we were able to multiply using these numbers in our heads because there were a lot of zeros which is the case with most even numbers. This is 981 2 using our method we came up with: (981) 2 = ( 900+81) (900+81) = 900 2 + 2(900x81) + 81 2 = 810000 + 145, 800 + 6561 = 962, 316 Even though we managed to get the answer there was no way that this could have been done without a calculator or pencil and paper because nobody can multiply 900 and 81 in their heads and no body can square 81 in their head which is the whole point of binomial expansion.

6. When is Long Multiplication more Efficient than Our Method?

8. (a+b) 2 = a 2 + 2ab + b 2