(8 mellanliggande sidversioner av 2 användare visas inte) Rad 1:
Rad 1: === Konjugatregeln ===
=== Konjugatregeln ===
{{lm2c|Konjugatregeln|22-24}}
Så här ser den ut:
: Så här ser den ut:
a<sup>2</sup>-b<sup>2</sup> = (a-b)(a+b)
utför multiplikationen:
(a - b)(a + b) = a<sup>2</sup> + ab - ba - b<sup>2</sup>
vi kan stryka ab - ba = ab - ab = 0:
(a - b)(a + b) = a<sup>2</sup> - b<sup>2</sup>
V.S.B.
=== Konjugatregeln med <math> <math>\LaTeX</math> </math> ===
: a<sup>2</sup>-b<sup>2</sup> = (a-b)(a+b)
: <math> (a-b) \cdot(a+b) </math>
Så här ser ''beviset'' ut med LaTeX:
: <math>= a^2 +a\cdot b -a\cdot b -b^2 </math>
:
: vi kan stryka ab - ba = ab - ab = 0:
<math> (a-b)\cdot(a+b) </math>
<math>= a^2 +a\cdot b -a\cdot b -b^2 </math>
<math>= a^2-b^2 </math>
<math>\blacksquare</math>
Tips ( skriv såhär i Wikitexten och googla typsättning med TeX för råd ):
: < math> = a^2-b^2 < /math>
<math>(a-b)\cdot(a+b)</math>
<math> = a^2 +a\cdot b -a\cdot b -b^2 </math>
<math> = a^2-b^2 </math>
<math> \blacksquare </math>
: V.S.B.
=== Film ===
=== Film ===
Rad 68:
Rad 46: <math>(a - b)\cdot(a + b) = a^2 - b^2 </math>
<math>(a - b)\cdot(a + b) = a^2 - b^2 </math>
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<html>
<iframe scrolling ="no " src ="https: //tube.geogebra.org /material /iframe /id /390017 /width /1188 /height /912 /border /888888 /rc /false /ai /false /sdz /true /smb /false /stb /false /stbh /true /ld /false /sri /true /at /auto " width ="1188px " height ="912px " style ="border:0px; "> </iframe>
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[http://www.geogebratube.org/material/show/id/390017 Länk till filen]
=== Uppgifter ===
=== Uppgifter ===
Rad 77:
Rad 59:
2. Lös <math>x^2-1=0</math> för alla reella x.
2. Lös <math>x^2-1=0</math> för alla reella x.
''Tips : Använd konjugatregeln och nollregeln för ekvationen.''
{{khanruta|'''Khan: Parentesmultiplikation'''
{{khanruta|'''Khan: Parentesmultiplikation'''
Konjugatregeln
Ma2C: Konjugatregeln, sidan
22-24
Så här ser den ut: a2 -b2 = (a-b)(a+b) [math]\displaystyle{ (a-b)\cdot(a+b) }[/math] [math]\displaystyle{ = a^2 +a\cdot b -a\cdot b -b^2 }[/math] vi kan stryka ab - ba = ab - ab = 0: [math]\displaystyle{ = a^2-b^2 }[/math] V.S.B. Film Bondestam (tv) respektive Matteboken (th) förklarar:
Geometriskt bevis av konjugatregeln Första beviset
Andra beviset
Visualisering
Här gäller:
[math]\displaystyle{ (x-y)\cdot(x+y) = x^2 - y^2 }[/math]
Denna är gjord med Geogebra, sparad som animerad gif, upladdad till WIKIMEDIA COMMONS och länkad hit.
[math]\displaystyle{ (a - b)\cdot(a + b) = a^2 - b^2 }[/math]
Länk till filen
Uppgifter Övningar (utan räknare)
1. [math]\displaystyle{ 1992\cdot 2008 = ? }[/math]
2. Lös [math]\displaystyle{ x^2-1=0 }[/math] för alla reella x.
Tips : Använd konjugatregeln och nollregeln för ekvationen.
Öva på Khan: Khan: Parentesmultiplikation
Hunnet så här långt kan vi repetera genom att lösa lite uppgifter på Khan Academy. De är dels av typen (a+b)(c+d) men också sådana som tillämpar kvadreringsregeln.
Khan om hur man multiplicerar binom ska du verkligen öva på.
Webbmatte
