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Updated Mar 24, 2026

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6 pages

Razstavljanje algebrskih izrazov z uporabo formul

Razstavljanje izrazov je kot razstavljanje sestavljanke - vzameš zapleteni izraz... Show more

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Kaj je razstavljanje izrazov?

Predstavljaj si, da imaš izraz kot 3x + 6 in ga želiš zapisati kot 3 $x + 2$ . To je razstavljanje - iz vsote naredimo produkt faktorjev. Je pravzaprav obraten postopek od množenja, kjer odpravljamo oklepaje.

Razstaviti izraz pomeni zapisati ga kot zmnožek dveh ali več faktorjev. Faktor je del, ki se pomnoži z drugim delom. Če preveriš s pomnožitvijo nazaj, moraš dobiti začetni izraz.

💡 Nasvet: Vedno preveri svoje delo! Pomnoži faktorje nazaj in vidiš, če dobiš začetni izraz.

Obstajajo trije glavni načini razstavljanja: izpostavljanje skupnega faktorja, uporaba razlike kvadratov in kvadrat dvočlenika. Najbolj osnoven je izpostavljanje, zato vedno začni s tem.

Izpostavljanje skupnega faktorja

Ta metoda deluje tako, da poiščeš največji skupni delitelj vseh števil in skupne spremenljivke z najnižjo potenco. To izpostaviš pred oklepaj.

Poglejmo primer 6a + 9b. Največji skupni delitelj števil 6 in 9 je 3. Skupnih spremenljivk ni. Torej: 6a + 9b = 3 $2a + 3b$ .

Pri izrazu 4x² - 8x je skupni delitelj števil 4, skupna spremenljivka pa x¹. Izpostaviš 4x: 4x² - 8x = 4x $x - 2$ .

⚠️ Pozor: Ne pozabi preveriti! 4x · x = 4x² in 4x · (-2) = -8x ✓

Postopek je preprost: poišči skupni del, ga zapiši pred oklepaj, nato vsak člen deli s tem skupnim delom in rezultat zapiši v oklepaj.

Razlika kvadratov

Formula a² - b² = $a - b$ $a + b$ je super pomembna in jo moraš znati na pamet! Deluje samo pri razliki (minus) dveh popolnih kvadratov.

Kako prepoznaš to situacijo? Imaš dva člena, med njima je minus, oba sta popolna kvadrata (lahko izračunaš koren iz njiju).

Primer x² - 49: Prvi člen x² ima koren x, drugi člen 49 ima koren 7. Torej a = x in b = 7. Uporabiš formulo: x² - 49 = $x - 7$ $x + 7$ .

❌ Pazi: Vsota kvadratov a² + b² se NE DA razstaviti na ta način!

Kvadrat dvočlenika prepoznaš po treh členih, kjer sta prvi in zadnji popolna kvadrata, srednji člen pa je enak 2ab. Primer: y² + 10y + 25 = $y + 5$ ².

Kombiniranje več metod

Pri zahtevnejših nalogah kombiniraš več korakov. Vedno najprej izpostavi skupni faktor, nato poglej, če se da še kaj razstaviti.

Primer 3x² - 75: Najprej izpostaviš 3, dobiš 3 $x² - 25$ . V oklepaju prepoznaš razliko kvadratov, zato nadaljuješ: 3 $x² - 25$ = 3 $x - 5$ $x + 5$ .

Pri 5a³ + 10a²b + 5ab² izpostaviš 5a in dobiš 5a $a² + 2ab + b²$ . V oklepaju prepoznaš kvadrat dvočlenika $a + b$ ².

🎯 Ključno: Ne pozabi na faktor, ki si ga izpostavil na začetku!

Končni rezultat: 5a³ + 10a²b + 5ab² = 5a $a + b$ ². Vedno sledi zaporedju: izpostavi → preveri oklepaj → uporabi formule → preveri rezultat.

Pregled glavnih pravil

Zaporedje korakov je ključno za uspeh. Najprej vedno poiščeš skupni faktor, nato preveriš, če ostane kaj, kar ustreza formulam.

Izpostavljanje deluje z največjim skupnim deliteljem števil in najnižjo potenco skupnih spremenljivk. Primer: 12xy - 8x² = 4x $3y - 2x$ .

Razlika kvadratov potrebuje minus in dva popolna kvadrata: 9 - y² = $3 - y$ $3 + y$ . Kvadrat dvočlenika prepoznaš po treh členih: x² - 14x + 49 = $x - 7$ ².

✅ Uspeh: Če si negotov, vedno pomnoži nazaj in preveri!

Razstavljanje ti bo pomagalo pri reševanju enačb in poenostavljanju ulomkov, zato si vzemi čas in vadite te tehnike. Z vajo postane avtomatsko!

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Matematika

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Updated Mar 24, 2026

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6 pages

Razstavljanje algebrskih izrazov z uporabo formul

Razstavljanje izrazov je kot razstavljanje sestavljanke - vzameš zapleteni izraz in ga razsekaš na enostavnejše dele, ki jih nato pomnožiš skupaj. To je super koristno, ker ti kasneje pomaga pri reševanju enačb in poenostavljanju ulomkov.

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Kaj je razstavljanje izrazov?

Razstaviti izraz pomeni zapisati ga kot zmnožek dveh ali več faktorjev. Faktor je del, ki se pomnoži z drugim delom. Če preveriš s pomnožitvijo nazaj, moraš dobiti začetni izraz.

💡 Nasvet: Vedno preveri svoje delo! Pomnoži faktorje nazaj in vidiš, če dobiš začetni izraz.

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Izpostavljanje skupnega faktorja

Ta metoda deluje tako, da poiščeš največji skupni delitelj vseh števil in skupne spremenljivke z najnižjo potenco. To izpostaviš pred oklepaj.

Poglejmo primer 6a + 9b. Največji skupni delitelj števil 6 in 9 je 3. Skupnih spremenljivk ni. Torej: 6a + 9b = 3 $2a + 3b$ .

Pri izrazu 4x² - 8x je skupni delitelj števil 4, skupna spremenljivka pa x¹. Izpostaviš 4x: 4x² - 8x = 4x $x - 2$ .

⚠️ Pozor: Ne pozabi preveriti! 4x · x = 4x² in 4x · (-2) = -8x ✓

Postopek je preprost: poišči skupni del, ga zapiši pred oklepaj, nato vsak člen deli s tem skupnim delom in rezultat zapiši v oklepaj.

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Razlika kvadratov

Formula a² - b² = $a - b$ $a + b$ je super pomembna in jo moraš znati na pamet! Deluje samo pri razliki (minus) dveh popolnih kvadratov.

Kako prepoznaš to situacijo? Imaš dva člena, med njima je minus, oba sta popolna kvadrata (lahko izračunaš koren iz njiju).

Primer x² - 49: Prvi člen x² ima koren x, drugi člen 49 ima koren 7. Torej a = x in b = 7. Uporabiš formulo: x² - 49 = $x - 7$ $x + 7$ .

❌ Pazi: Vsota kvadratov a² + b² se NE DA razstaviti na ta način!

Kvadrat dvočlenika prepoznaš po treh členih, kjer sta prvi in zadnji popolna kvadrata, srednji člen pa je enak 2ab. Primer: y² + 10y + 25 = $y + 5$ ².

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Access to all documents

Improve your grades

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Kombiniranje več metod

Pri zahtevnejših nalogah kombiniraš več korakov. Vedno najprej izpostavi skupni faktor, nato poglej, če se da še kaj razstaviti.

Primer 3x² - 75: Najprej izpostaviš 3, dobiš 3 $x² - 25$ . V oklepaju prepoznaš razliko kvadratov, zato nadaljuješ: 3 $x² - 25$ = 3 $x - 5$ $x + 5$ .

Pri 5a³ + 10a²b + 5ab² izpostaviš 5a in dobiš 5a $a² + 2ab + b²$ . V oklepaju prepoznaš kvadrat dvočlenika $a + b$ ².

🎯 Ključno: Ne pozabi na faktor, ki si ga izpostavil na začetku!

Končni rezultat: 5a³ + 10a²b + 5ab² = 5a $a + b$ ². Vedno sledi zaporedju: izpostavi → preveri oklepaj → uporabi formule → preveri rezultat.

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Access to all documents

Improve your grades

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Pregled glavnih pravil

Zaporedje korakov je ključno za uspeh. Najprej vedno poiščeš skupni faktor, nato preveriš, če ostane kaj, kar ustreza formulam.

Izpostavljanje deluje z največjim skupnim deliteljem števil in najnižjo potenco skupnih spremenljivk. Primer: 12xy - 8x² = 4x $3y - 2x$ .

Razlika kvadratov potrebuje minus in dva popolna kvadrata: 9 - y² = $3 - y$ $3 + y$ . Kvadrat dvočlenika prepoznaš po treh členih: x² - 14x + 49 = $x - 7$ ².

✅ Uspeh: Če si negotov, vedno pomnoži nazaj in preveri!

Razstavljanje ti bo pomagalo pri reševanju enačb in poenostavljanju ulomkov, zato si vzemi čas in vadite te tehnike. Z vajo postane avtomatsko!

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We thought you’d never ask...

What is the Knowunity AI companion?

Where can I download the Knowunity app?

You can download the app in the Google Play Store and in the Apple App Store.

Is Knowunity really free of charge?

That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.

Smart Tools NEW

Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Practice Test ✓ Essay Outlines

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App Store

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Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Thomas R

iOS user

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

Elisha

iOS user

Paul T

iOS user

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Thomas R

iOS user

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

Elisha

iOS user

Paul T

iOS user