Kuthunyelwe ngu UDebora Silva

Ixesha lokuma, okanye i-algebraic, naliphi na ibinzana le-algebra elinokuphindaphindwa kuphela phakathi kwamanani kunye nokungaziwa (oonobumba abamele amanani angaziwayo). Yeyona ndlela ilula yokubonisa i-algebra kwaye inokuqondwa njenge-polynomial enekota enye.

Ukusetyenziswa kweekhonsepthi kumanqwanqwa okuqala ukusuka ekwenziweni kwezinto (njengebhola, umzekelo) ukuya kubalo oluntsonkothileyo.

Igqwetha elinguFrançois Viète lalinoxanduva lokusebenzisa oonobumba kubudlelwane bemathematika, obuvumela ukubala kwe-algebra kunye nophuhliso lwemathematika kunye nesayensi.

Isalathiso semixholo

Athini amalungu omtshato omkhulu?

Ukuqonda i-monomials, kufuneka sazi iinxalenye zazo. Zahlulwe zangamacandelo amabini: inani, elibizwa ngokuba ngumlingani womlinganiso womntu omnye; kunye nemveliso eguquguqukayo okanye imveliso (iileta).

Nika ingqalelo kule mizekelo ilandelayo:

• 4y: kule monomial, sinokubona ukungalingani (4) kunye nenxalenye yokoqobo (y).
• X - Qaphela ukuba, kule monomial, akukho manani acacileyo. Kule meko, ukungalingani kuya kuhlala kungu-1. Inxalenye yokoqobo yileta x.
• Kubalulekile ukuba uqaphele ukuba kusekho iimeko apho indawo yokoqobo ilahlekileyo, kwaye kuphela ukungqinelana kwamanani okuvela. Kuyinto enkulu ngaphandle kwenxalenye yokoqobo. Ukuba kuphela sinenombolo engu-zero, ngaphandle kwenxalenye yokoqobo, ililize kuphela.

Iimpawu ezifanayo

Njengoko sele sibonile, monomial nganye yahlulwe yangamacandelo amabini: indawo yokoqobo kunye nokulingana. Ukuba ezimbini okanye ngaphezulu ii-monomials zinenxalenye efanayo yokoqobo, zi-monomials okanye amagama afanayo.

Imizekelo:

-5yz kunye ne-½ yz zii-monomials ezifanayo, kuba zinenxalenye efanayo yokoqobo (yz).
-x kunye ne-2x zikwimo efanayo yemonomials, kuba icandelo lokoqobo lilingana (x).

Ukongezwa kweAlgebra kunye nokukhupha ii-monomials

IiMonomials zinokongezwa kuphela okanye zithatyathwe xa iinxalenye zazo zifana. Ukwenza lo msebenzi, yongeza nje ii-coefficients kwaye uphinde icandelo lokoqobo.

Jonga ngononophelo kulo mzekelo ulandelayo:

-4xy + 16xy = 20xy

Ukuthabatha kwenziwa ngendlela efanayo:

-25xy - 3xy - 5xy = 17xy.

Phinda-phinda uze wahlule ii-monomials

Ukwenza ukuphindaphinda kunye nokwahlulahlula ii-monomials, akufuneki zifane. Ngokungafaniyo nokudibanisa nokuthabatha, le misebenzi kufuneka yenziwe kunye nenxalenye yokoqobo kunye nokulingana. Kuya kufuneka sisebenzise ii-coefficients komnye komnye kwaye indawo yokoqobo yelinye yecandelo lokwenyani lenye. Khumbula ukuba ii-exponents kufuneka zongezwe.

Jonga le mizekelo ilandelayo:

-6x²y.2x³.3y Kule, siphinda-phinda 6.2.3 = 36 kwaye siphinda-phinda x².x³.yy = x5.y²

Ngokwahlulayo, kufuneka sahlule ii-coefficients phakathi kwabo, ngendlela efanayo nenxalenye yokoqobo:

-12x4y / 3x2y -> 12/3 = 4; icandelo lokoqobo: x4 / x² = x² kunye y / y = 1, ukunika isiphumo esilingana no-4x².