Binomial expansions reflection. Denise 8A. Our method. In our investigation, we came up with a general rule for expanding binomials, particularly in squaring the sum and difference of two terms: (a + b) 2 = a 2 + 2ab + b 2 and (a – b) 2 = a 2 – 2ab + b 2.
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In our investigation, we came up with a general rule for expanding binomials, particularly in squaring the sum and difference of two terms:
(a + b)2 = a2 + 2ab + b2 and
(a – b)2 = a2 – 2ab + b2
This method would have been useful to an engineer 100 years ago because is was quicker than long division, as well as easy to use and less likely to confuse you.Say you needed to find the square of 672. instead of using long division to figure out all those numbers, you just use our quick method.
In some parts of our method (see b2), you still have to use long multiplication because if you had a large number for b or a then you would have to use long multiplication to find the answer. For example, in the working of trying to find the square of 672:
(10 + 662) (10 + 662)
100 + 6,620 + 6,620 + 662 x 662
What?!?! What was that? That would be the part where you would have to still use long multiplication, making the process cumbersome.
Long multiplication would have been more useful than our method when using numbers less than one, because the method doesn’t work for numbers less than one. By this, I mean numbers like 0.73, not numbers like -6. for example, the method didn’t work with 0.99 on the test.