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This presentation, led by Umema Khan from 8C PS, explores the concept of binomial expansion, particularly illustrating the formula (a+b)² = a² + 2ab + b² and (a-b)² = a² - 2ab + b². Through an investigation, we demonstrated how binomial expansion can simplify calculations but also identified scenarios where traditional multiplication may be more effective. Notably, we addressed examples involving large numbers, decimals, and specific conditions that challenge the efficiency of binomial expansion. Join us in uncovering the nuances of this mathematical technique!
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Binomial Expansion Reflection By: Umema Khan 8C P.S. please play the slideshow because there is sound
Recently Concluded We have Recently concluded an investigation in which we looked at (0.99)2 = (1-0.01)(1-0.01) = 1 2- 2 x 1 x 0.01 + 0.012. We then came up with the general rule that (a + b)2 = a 2 +2ab +b 2 and (a - b) 2 = a 2 - 2ab + b 2
100Yearsago… 1122 =(100 + 12) (100 +12) = (1002)+ (2 x100) + (2 x12) + (122) = 10000 + 1200 +1200 + 144 = 12544 And the engineer would have to build a house which’s area is within 12544 yards2
But... But this isn’t always the case there are some places where long multiplication would have actually been a lot easier like: • If the number has 2 or more decimals places plus a whole number • If there is a number does not end in a zero • If the number has more than 4 digits and does not at all contain a zero • If the number is in the middle of two numbers (like 153 is in between 100, and 200) • If you do not square, there are two different numbers multiplied together
For Example: 1532
This therefore proves that the binomial expansion method can become tricky if it is not used in the right times and that it can only help to a certain extent.
