zoobyshoe said:
The sum of a2 + 2ab + b2? That one?
It's a little more involved, but looks pretty impressive to others if they do not know you're using it.
Take a, as the number to be squared. Then the method consists of :
1)Adding b to a, getting a+b
2)Subtracting b from a, to get a-b ( We always take b<a)
3)Squaring b, to get b^2.
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4)We then find a^2 by multiplying (a+b)(a-b) , and then adding b^2 to this.
( Note : (a+b)(a-b)+b^2 =a^2-b^2+b^2= a^2+(b^2-b^2)=a^2 ; simple but powerful).
The key idea is to make a wise choice for b .
A couple of examples:
Example 1)Take a =988, so we want to calculate 988^2
2)We choose a value b , and calculate a+b and a-b .The idea is to choose b wisely. In this case, b=12 is helpful, since a+b =1000, so we multiply by 1000, which is equivalent to tacking zeros at the end. Then a-b is 976, and b^2 =144.
So we have:
988^2 =(988+12)(988-12)+12^2 =(976)(1000)+12^2 =976000+144=976144
(Check with your calculator!).
Example 2)
Take a=113 , to find 113^2 . We choose b=13 , since a-b =100 . Then:
1)a+b =113+13=126
2)a-b =113-13=100
3)b^2 =13^2 =169
Then we calculate : (a+b)(a-b)+b^2 = (126)(100)+13^2 =12600+169=12769
Note that this trick works better with some numbers than others, but with some practice you can use it for all numbers.
Let's practice, what is :
i)198^2
ii) 311^2
iii) (XMV)^(II) ?
. But it wasn't as boring as it sounds. It focused a lot on colors bouncing off the soap bubbles.
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Yes, I totally agree. To be straight, I don't think my salary will get changed even after I bring this up to our HRers and directors because the difference I expect is too far from the current level(current+current*1/2.2). I have friends and they let me read their next job offers along with their current job's payslips sent monthly from our directors in charge. I am shocked and was stupid to negotiate a lower price for myself. Bluntly, I am now looking for another job.
