Patterns with squaring numbers.
Ok, I was wicked bored one day, and I noticed that I found a system for finding the difference between squared numbers without squaring them. The formula is:
markup(n1+n2)*(n2-n1)For example, i'll use 5 and 10:markup(5+10)*(10-5)= 15*5=75now to check the answer:markup5^2=25 10^2=100 100-25=75if you dont belive me, try it yourself. it works for every number. If someone could explain the logic behind it (or try it and tell me that it works or doesn't) or something, that'd help.
yes, i did make this formula myself, although i'm sure other people found it also.
n30 wrote: Ok, I was wicked bored one day, and I noticed that I found a system for finding the difference between squared numbers without squaring them. The formula is:
markup(n1+n2)*(n2-n1)For example, i'll use 5 and 10:markup(5+10)*(10-5)= 15*5=75now to check the answer:markup5^2=25 10^2=100 100-25=75if you dont belive me, try it yourself. it works for every number. If someone could explain the logic behind it (or try it and tell me that it works or doesn't) or something, that'd help.
yes, i did make this formula myself, although i'm sure other people found it also. It's quite simple actually. Your formula can be written another way, if expanded.
= n1*n2 - n1*n1 + n2*n2 - n2*n1
= n1*n2 - n1*n2 + n2^2 - n1^2
= n2^2 - n1^2```
I used some spacing to make things easier to read, it doesn't change the mathematics
There you have it, you are left with finding the difference by squaring both numbers. In the end, you really are squaring the numbers; you just need to understand how simplification works.
lol, nice, dude, no your not the first, what you found is called the difference of two squares, get it? lol. It's a way to factorise equations like x^2-y^2 to (X-y)(x+y).
It's quite simple actually. Your formula can be written another way, if expanded.
(n1+n2)(n2-n1) = n1n2 - n1n1 + n2n2 - n2n1 = n1n2 - n1*n2 + n2^2 - n1^2 = n2^2 - n1^2
I used some spacing to make things easier to read, it doesn't change the mathematics
There you have it, you are left with finding the difference by squaring both numbers. In the end, you really are squaring the numbers; you just need to understand how simplification works.
You may be able to reduce it to a simple equation but thats hwy it's so useful. It can be used to factoise any binomial. (if you are willing to have surds and negative roots and complex numbers)