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Binomial Expansion

Binomial Expansion. By Rebecca Hitchman. If you were an engineer 100 years ago, explain how our method may have been useful rather than just using long multiplication? . The method ( a+b) 2 = a 2 + 2ab + b 2 and ( a-b) 2 = a 2 – 2ab + b 2

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Binomial Expansion

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  1. Binomial Expansion By Rebecca Hitchman

  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 (a+b) 2 = a2 + 2ab + b2and (a-b) 2 = a2 – 2ab + b 2 would have helped an engineer because instead of doing (a+b) x (a+b) because a might be 12 and b might be 32 so instead of doing 12 x 32 + 12 x 32 they would know that the answer would just be 122 +2x(12x32)+ 322. Since 12 x 12 are part of simple multiplication (144) and half of 32 is 16 only 4 more then 12 (so it would be 12x16 + 12x16 = 12 x32) the problem becomes a lot simpler.

  3. At what point would this method be big and cumbersome? I would think twice about using this method (Binomial expansions) if the number was in the 1000 or in the 1000ths decimal place or larger this way ((a+b) 2) would be very hard and it would probably be easier to just work it out using long multiplication.

  4. When would I not use this method? • Level 5-6: If I had to figure out the area of a square patch of grass and I had it in cm and it was about 5000 cm I would use long multiplication instead of this method because I think it would be more accurate. • This method: (5000)2 = (4000+1000) (4000+1000)= 16,000,000+4,000,000+4000,000+1000,000= 20,000,000+5,000,000 =25,000,000 5000 x 5000 0000 00000 000000 25000000 5,000 5,000

  5. Another example of when I would not use this method. If I had to find the area of a tile to see how many I would need to fit my bathroom and the tile was (2321)2 mm. I would use long multiplication because (2300+21)(2300+21)=23002+2x(2300x21)+212 is more open to mistakes. 2321 x 2321 2321 46420 696300 4642000 5387041 2321 mm 2321 mm

  6. So in conclusion… • So even though the binomial expansion is a good method and is useful for squaring numbers I wouldn’t use it when the numbers are smaller than the 1000ths decimal place and bigger than 1000 since using long multiplication is easier.

  7. Thank You

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