Algebra – Binomials & Polynomials – Addition and Substraction
Binomial – Addition
We all know how to make an addition with any regular number, so here is a tutorial on how to make an addition with a Binomial.
x² – 2² + 9x² – 2²
2(x+2) (x+2)
The first thing to do is to simplify the numerator of both fraction :
1)
x² – 1 = (x – 2) (x + 2)
2(x+2) (x+2)
and now the second fraction :
2)
9x² – 2² = (3x – 2) (3x + 2)
(x+2) (x+2)
So now we have :
= (x – 2) (x + 2) + (3x – 2) (3x + 2)
2(x+2) (x+2)
(x + 2) is a common factor for both fractions and if you look a little more closer you can see that you can simplify (x +2) for the first one :
= (x -2) (x + 2) + (3x – 2) (3x + 2)
2(x + 2) (x +2)
And now to make an addition of these term, we multiply them by the missing term in the denominator just like this :
= (x -2) x (x +2) + (3x – 2) (3x + 2) x 2
2 x (x+2) (x + 2) x 2
= (x² + 2x – 2x – 4) + (18x² + 12x + 12x +8)
2(x+2)
= 19x² + 24x + 4
2(x + 2)
Voila.
I hope that you liked it and that it was really useful. Next time i will make a tutorial with a polynomial with substraction thank you for reading this and don’t hesitate to leave a comment if there is any error or if you need explanation.
Jordan Landao
Algebra – Binomials and Polymials – Basics
Monomial
Here is a quick tutorial on how to factor a Binomial and a Polynomial.
The first thing to do is to find a common term within the equation and it depend on what kind of equation you have, for exemple let’s start with an easy Binomial :
49x²-9y²
here to simplify we can transform 49 to (7²) because (7×7) equal (49) and in order to factorize this Binomial we need at least to perfectly divide it in this case, because there is no common factor between them.
And we can do the same for 9 which is (3²).
Now we have (7²x² – 3²y²) and what we gonna do here is to split it in two equal Binomial :
= (7x + 3y) x (7x – 3y)
Let’s see if we have the correct anwser :
(7x + 3y) x (7x – 3y) =
= (49x² – 21xy + 21xy – 9y²) and (-21xy + 21xy = 0)
= (49x² – 9y²)
So the anwser is (7x + 3y) x (7x – 3y).
The reason why we could split it in two is because of the negative sign ”-”.
If we had (49x² ”+” 9y²) it would be another equation.
(49x² ”+” 9y²) =
= (7²x² + 3²y²)
= (7x + 3y) (7x + 3y) =
= (49x² + 21xy + 21xy + 9y²)
= (49x² +42xy + 9y²). Voila.
Polynomial
Now let’s try with a Polynomial :
(-3x²yz² -6xyz + 4x³yz² + 8x²yz) =
-3xyz(xz + 2) 4x²yz(xz + 2) =
(-3xyz + 4x²yz) (xz +2) =
= xyz(4x – 3) (xz + 2). Voila.
So that’s it for this little tutorial, next time i’ll do something a little bit more complicated with addition, substraction, division and multiplication.
Hope you liked it and if a made any error, nobody gonna die, just tell me :).
Jordan Landao
Basic With History of the Atom – Atom Discovery
Atom Discovery ”Atomos”
History of the atom
The word Atom mean ” indivisible” which come from the old Greek ”Atomos”, a word created by ”Leucipe” (460-370 B.C) who claim that all the matter surrounding us is made of tiny particle, so little that they cannot be separated nor seen with the eye.
Democritus (460-370 B.C) his disciple said some years later that not only the matter is made of tiny particle can combine togheter and that there is ”space” between them. They cannot be separated but still they are.
Aristotle (384-322 B.C) and Empedoclus (490-435 B.C), even if they were great thinkers at the time, did not approve the theory started by Leucippus and followed by his disciple Democritus. Instead, they believed that matter was made of four basic elements : Water, Wind, Earth, Fire, and the different combination of them can create any substance, that we are made of these element, we, human being and animals too, under the action of the four fundamental which are Hot, Dry, Wet and Cold.
John Dalton (1766-1844) came with the idea, after numerous observation and experience, that there is two distinct type of elements composing the matter or any substance : elements and compounds.
Elements are made of the same (single or more) atoms while Compounds are made of different atoms (at least two) sticking togheter by bond. Compounds are either Monoatomic (alone, Ne, Na) or Diatomic (by set of two, Ne2, Cl2, O2). The elements of the same type have the same mass while, the others elements have a different mass.
I tried to the best of my actual english vocabulary to explain everything correctly. Thank you very much for reading my article and i will be back with more food for the brain, i hope that you liked it.
Jordan Landao
Nuclear Fusion – Fusion Nucléaire
(ENGLISH)
NUCLEAR FUSION
Nowadays, it is clear that this is more than a matter of time. What is it? The nuclear fusion of course! Clean energy, safe for humans and produces phenomenal amounts of energy just.
No one has yet managed to maintain this nuclear reaction is effectively merging, but research we demonstrate that it is a dream that will soon become a reality.
This technology is fascinating, because it is a simple solution that even if it poses a few problems at the level of heat according to the most ancient studies (which is no more a problem), it is harmless to human beings human as well as the environment, providing both large quantities of energy.
Nuclear fusion is a phenomenon that is not spontaneous. The Sun is used as a model to create thermonuclear fusion, which may exceed the 150 000 000 degrees Celsius within the Sun.
It is a simple process that is totally opposite to the merger: deuterium and the lithium6 * (who at the absorption of a neutron in the nucleus turns into tritium) fusion is possible in the reactor or as long as the requirements are applied, continues:
- * Deuterium deuterium → (Helium-3) + (neutron) + energy
- * Deuterium deuterium → (Tritium) + (proton) + energy
- * Deuterium + tritium → (Helium 4) + (neutron) + energy
- * deuterium, helium 3 → (Helium 4) + (proton) + energy
- * for the Lithium6 *.
Nuclear fusion
The Tritium is an isotope of hydrogen that at the level of its availability on Earth is found in enough quantity to supply the Earth with energy for 100 000 000 million years (1 cubic meter of water can provide as much energy as the burning of 700 tonnes of oil. It is 3 to 4 times more energy that can be produced by the fusion of light atoms for the same mass of fuel used for nuclear fission.
Some applications & comparison
I’m of the opinion that the fusion (cold fusion) has many applications and is the future, because it is much more advantageous that classic, even if merging others stubbornly want to continue their dangerous experiments on fission: they have totally wrong to want to continue such experiments, knowing the risks to human nature and the species.
- Firstly due to the fact that it emits no radiation, toxic waste and that it is not dangerous or harmful to the environment or to human beings human.
- Secondly, it can be implemented anywhere: whether in our homes, in our cars, buses, boats or planes with this new technological innovation there is no risk,. Unlike fossil fuels.
- And thirdly, it is a whole arsenal of devices that could benefit from… cold fusion! Cold fusion is a reaction that can be caused at room temperature, unlike the merge that you could say classic. It requires very little energy and is carried out at room temperature. They are safe (fusion and cold fusion), because in case of accident, the temperature is quickly returning to normal and elements present in the reactor are escaping into the air that already contains, so they produce no damage.
I am for the use and research into nuclear fusion, because even if some are of the opinion that this is always that fairytale despite all evidence, including cold fusion recently, discovered the huge amounts of energy produced by the attempts of failed mergers * and the many benefits of this technology which emits no pollutant harmful to health or the environment or nuclear waste further, it is a reality that we must accept and stop using fossil fuels or radioactive energy although it is masteredto live in a better world. I hope that humanity can move in the right direction as many of us.
When will we finally understand?
Jordan Landao
(FRENCH)
LA FUSION NUCLÉAIRE
De nos jours, c’est évident que ce n’est plus qu’une question de temps. De quoi s’agit-il? De la fusion nucléaire bien sûr! Une énergie propre, sans danger pour l’homme et qui produit des quantités d’énergie phénoménales tout simplement.
Personne n’a encore réussi à maintenir ce mode de réaction nucléaire qu’est la fusion de manière efficace, mais les recherche nous démontrent que c’est un rêve qui deviendra bientôt une réalité.
Cette technologie est fascinante, car c’est une solution simple qui même si elle pose quelques problèmes au niveau de la chaleur selon les plus anciennes études (ce qui n’est plus un problème), elle reste inoffensive pour les êtres humains ainsi que l’environnement en procurant à la fois de grandes quantités d’énergie.
La fusion nucléaire
La fusion nucléaire est un phénomène qui n’est pas spontané. Le soleil est utilisé comme modèle pour créer la fusion thermonucléaire, qui au sein du soleil peut dépasser les 150 000 000 de degrés Celsius.
C’est un procédé simple qui est totalement inverse à la fusion : c’est avec du deutérium et du lithium6* (qui lors de l’absorbation d’un neutron dans le noyau se transforme en tritium) que la fusion est possible dans le réacteur ou tant que les conditions requises sont appliquées, se poursuit :
- * Deutérium + deutérium → (Hélium 3) + (neutron) + énergie
- * Deutérium + deutérium → (Tritium) + (proton) + énergie
- * Deutérium + tritium → (Hélium 4) + (neutron) + énergie
- * deutérium + hélium 3 → (Hélium 4) + (proton) + énergie
- * Pour le Lithium6*.
Le Tritium est un isotope de l’Hydrogène qui au niveau de sa disponibilité sur terre, est retrouvée en quantité assez suffisante pour alimenter la terre en énergie pendant 100 000 000 millions d’années (1 mètre cube d’eau peut fournir autant d’énergie que la combustion de 700 tonnes de pétrole. C’est 3 à 4 fois plus d’énergie qui peut être produite par la fusion d’atomes légers pour la même masse de combustible utilisée pour la fission nucléaire.
Certaines applications & Comparaison
Je suis d’avis que la fusion (la fusion froide) possède de nombreuses applications et est l’avenir, car elle est beaucoup plus avantageuse que la fusion classique, même si d’autres s’entête à vouloir poursuivre leur expérimentations dangereuses sur la fission nucléaire : ils ont totalement tort de vouloir poursuivre de telles expérimentations, connaissant les risques pour la nature et l’espèce humaines.
- Premièrement dû au fait qu’elle n’émet aucune radiation, déchet toxique et qu’elle n’est pas dangereuse ou nocive pour l’environnement ou pour les êtres humains.
- Deuxièmement, elle peut être implantée n’importe où : que ce soit dans nos foyers, dans nos voitures, dans les autobus, les bateaux ou les avions avec cette nouvelle innovation technologique il n’y a aucun risque, contrairement au combustibles fossiles.
- Et troisièmement, c’est tout un arsenal d’appareils qui pourraient bénéficier de la fusion… froide! La fusion froide est une réaction qui elle peut être provoquée à température ambiante, contrairement à la fusion que l’on pourrait dire classique. Elle ne requiert que très peu d’énergie et se réalise à température ambiante. Elles sont sans danger (fusion et fusion froide), car en cas d’accident, la température est vite de retour à la normale et les éléments présents dans le réacteur s’échappent dans l’air qui en contient déjà, donc ils ne produisent aucuns dégâts.
Je suis pour l’utilisation et la recherche sur la fusion nucléaire, car même si certains sont d’avis que ce n’est toujours qu’un conte de fée malgré toutes les preuves, notamment la fusion froide découverte récemment, les quantités énormes d’énergie produites par les tentatives de fusions ratées* et les nombreux bienfait de cette technologie qui n’émet pas de polluant nocif pour la santé ou l’environnement ou de déchet nucléaire quelquonques, c’est une réalité qu’il faut accepter et cesser d’utiliser les combustibles fossile ou l’énergie radioactive même si elle est maîtrisé, pour vivre dans un monde meilleur. Je souhaite que l’humanité puisse avancer dans la bonne direction comme beaucoup d’entre nous.
Quand comprendrons-nous enfin?
Jordan Landao
BIBLIOGRAPHIE
TRITIUM – Wikipedia
* (en) CiffroyP., Siclet F., Damois C., LuckM., A dynamic model for assessing radiological consequences of tritium routinely released in rivers. Application to the Loire River ; Journal of Environmental Radioactivity, Volume 90, Issue 2, 2006, Pages 110-139
* (en) Livshits Alexander I.; Hatano Yuji; Watanabe Kuniaki (2002) ; Superpermeability in fusion technology : Tritium accumulation and compression ; Fusion science and technology ; Congrès / International Conference on Tritium Science and Technology No6, Tsukuba, JAPON (12/11/2001) ;2002, vol. 41 (2), no 3 (880 p.) pp. 882-886 (résumé INIST/CNRS)]
* (en) Raskob, W, Strack S, FZK-Autoren, U.A. Tritium in the food chain. Comparaison of predicted and observed behaviour. A. Re-emission from soil and vegetation. B. Formation of organically bound tritium in grain of spring wheat, Biomovs II Technical Report no 13, septembre 1996.
* (en) Raskob, W, Strack S, FZK-Autoren, U.A. Tritium in the food chain.Intercomparison of model predictions of contamination in soil, crops, milk and beef after a short exposure to ttitiated water vapour in air, Biomovs II Technical Report no 8, septembre 1996.
* (en) Raskob, W, Diabate S, Strack S, A new approch for modelling teh formation and translocation of organically bound tritium in accident consequence assessment, codes Internat. Symp on Ionizing Radiation: Protection ot the natural Environment, Stockholm, S, may 20-24, 1996. * (en) études sur la production de tritium (avec ScienceDirect)
FUSION NUCLÉAIRE-Wikipedia
* (en) Cornelius Marius Braams, Peter E. Stott, Nuclear Fusion, New York, CRC Press, 2002 (ISBN 978-0-7503-0705-5) (aperçu limité en ligne)
* (en) Stefano Atzeni, Jürgen Meyer-ter-Vehn, The Physics of Inertial Fusion: Beam Plasma Interaction, Hydrodynamics, Hot Dense Matter, Oxford, Oxford University Press, 2004 (ISBN 978-0-19-856264-1) (aperçu limité en ligne) * (fr) Centre d’étude de l’Énergie Nucléaire * (fr) Fusion magnétique, dossier du CEA * (en) Agence internationale pour l’énergie atomique
La fusion nucléaire dans un appartement http://lefilpresse.wordpress.com/2012/11/09/la-fusion-nucleaire-dans-un-appartement/
LE TRITIUM C’EST QUOI ? http://www.cnsc-ccsn.gc.ca/fr/readingroom/tritium/tritium_studies_faq.cfm
Fission et fusion nucléaires http://bambou254.over-blog.com/article-fusion-nucleaire-energie-propre-et-sans-danger-45417713.html
Science & Atom - We must understand 