Muab tso rau los ntawm Debora Silva

Monomial, lossis lub sij hawm algebraic, yog ib qho kev qhia lej algebra uas tsuas muaj kev sib npaug ntawm cov lej thiab tsis paub (cov tsiaj ntawv uas sawv cev cov zauv uas tsis paub). Nws yog daim ntawv uas yooj yim tshaj plaws ntawm algebraic expression thiab tuaj yeem nkag siab ua polynomial uas tsuas muaj ib lo lus nkaus xwb.

Kev siv ntawm lub tswv yim ntawm cov monomials nyob ntawm qhov tsim cov khoom (xws li lub pob, piv txwv) mus rau ntau cov kev suav hnyav.

Tus kws lij choj François Viète yog lub luag haujlwm ntau rau kev siv cov tsiaj ntawv hauv cov kev sib raug zoo hauv kev ua lej, uas tau tso cai rau kev suav lej thiab kev txhim kho kev ua lej thiab kev tshawb fawb.

Txheem ntsiab lus

## Dab tsi yog seem ntawm monomial?

Txhawm rau kom nkag siab txog monomials, peb yuav tsum paub txog lawv feem. Lawv tau muab faib ua ob ntu: tus lej, hu ua monomial coefficient; thiab cov khoom sib txawv lossis cov khoom lag luam ntawm cov tsiaj ntawv (ntawv).

Ua tib zoo mloog rau cov piv txwv nram qab no:

• 4y: hauv no monomial, peb tuaj yeem pom cov coefficient (4) thiab ntu ntu (y).
• X - Nco ntsoov tias, hauv monomial no, tsis muaj cov lej tsis meej. Hauv qhov no, lub coefficient yuav ib txwm yog 1. Qhov muaj tiag tiag yog tus ntawv x.
• Nws yog ib qho tseem ceeb kom nco ntsoov tias tseem muaj cov xwm txheej uas qhov feem ntawm qhov ploj lawm, thiab tsuas yog cov lej coefficient tshwm. Nws yog monomial tsis muaj ntu ncaj nruab nrab. Yog tias peb tsuas muaj tus lej xoom, tsis muaj qhov ncaj nruab nrab, nws yog null monomial.

## Zoo sib xws monomials

Raws li peb twb pom, txhua lub monomial tau muab faib ua ob ntu: ntu ntu thiab coefficient. Yog tias ob lossis ntau dua monomials muaj qhov zoo tib yam lus, lawv yog monomials lossis cov ntsiab lus zoo sib xws.

Piv txwv:

-5yz thiab ½ yz zoo ib yam li monomials, vim tias lawv muaj tib ntu (yz).
-x thiab 2x kuj yog cov monomials zoo ib yam, txij li cov ntu cia sib npaug (x).

## Algebraic ntxiv thiab rho tawm ntawm cov monomials

Monomials tsuas tuaj yeem muab sib ntxiv los yog rho tawm yog tias lawv cov seem yog tib yam. Los ua qhov kev ua haujlwm, tsuas yog ntxiv cov coefficients thiab rov hais dua qhov tseeb.

Saib kom zoo zoo nyob rau hauv cov piv txwv hauv qab no:

-4xy + 16xy = 20xyooj

Qhov rho tawm tiav yog ua tib txoj kev:

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

## Faib thiab faib cov monomials

Txhawm rau ua cov sib npaug thiab faib cov monomials, lawv tsis tas yuav muaj qhov zoo sib xws. Tsis zoo li kev sib ntxiv thiab rho tawm, cov haujlwm no yuav tsum tau ua nrog ob qhov tib si thiab qhov sib npaug. Peb yuav tsum muaj cov coefficients rau ib leeg thiab ib ntu ntawm ib qho rau qhov ncaj ntawm lwm tus. Nco ntsoov tias cov exponents yuav tsum tau ntxiv.

Saib rau ntawm cov piv txwv nram qab no:

-6x²y.2x³.3y Hauv qhov no, peb ntau 6.2.3 = 36 thiab muab x².x³.yy = x5.y²

Hauv kev faib, peb yuav tsum faib cov coefficients nruab nrab ntawm lawv, tib txoj kev raws li qhov tiag tiag:

-12x4y / 3x2y -> 12/3 = 4; qhov ncaj ncees ntu: x4 / x² = x² thiab y / y = 1, muab qhov tshwm sim sib npaug rau 4x².