Rad 46:
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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[http://www.geogebratube.org/material/show/id/390017 Länk till filen]
=== Uppgifter ===
=== Uppgifter ===
Nuvarande version från 28 januari 2015 kl. 20.54
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
