@ Mathematicians (and friends):
If:
(a + b) (a + b) = A = a2 + 2ab + b2
(a – b) (a – b) = B = a2 – 2ab + b2
(a + b) (a – b) = C = a2 – b2
does
D = -a2 – 2ab – b2
E = -a2 + 2ab – b2
exist?
If yes, what should one write left of D, E? Why is a question about that not teached?
Are there more miracles by the binoms? Are they logical if the inverse rule does it too? For the logical inverse see: Martinez, negative math.
If nobody is interested to reveal the secret, given by the about 2,500 years old tower-building of the Babyloniens as a fundament in mathematics, here, then this question will be deleted soon. One only will get information at my homepage (www.mathe-neu.de) in future.
@ Wiwat Wanicharpichat
Dear Wiwat,
thanks for answer. In D = -A correct; in E = -B correct too.
One may think that this are obsolete forms of the same in A and B.
But the terms -A and -B look different to A and B because it only changes the prefixes in one of the two factors. If A is given by: x * x then follows, that -A is given by -x * x = -x2 . If we now want to know what x is, we have to take the square-root. Would that be part of complex theory with square-root of minus one?
If we had to learn the binoms to have their solutions by heart, we must learn this forms too.
If only the principle is interesting, we did enough with the second one. In that there is all in combination: `+´ by `+´; `+´ by `–´; `–´by `+´; `–´ by `–´ .
Another question is, what an effect in effectivity we get by the binoms.To get the solution one has, from left to right, to carry out 3 (or only 2 if addition is taken for both factors and then multiplication) calculations in A and B left of A and B but 6 calculations right of A and B. Only for C it is equal.
What about Martinez?
Are you interested in the other parts of my question?
Regards, Peter Kepp
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