Lösung 2.1:2d - Versionsgeschichte

Moni: Rechtschreibung

2009-08-04T14:06:04Z

Rechtschreibung

← Nächstältere Version		Version vom 14:06, 4. Aug. 2009
Zeile 10:		Zeile 10:
	{{Abgesetzte Formel\|\|<math>(9x^4-4)(9x^4+4)=(9x^4)^2-4^2=81x^8-16\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>(9x^4-4)(9x^4+4)=(9x^4)^2-4^2=81x^8-16\,\textrm{.}</math>}}

-	Hinweis: Wir hätten auch gleich alle Klammern miteinander multiplizieren können, aber die Rechnungen ~~währen~~ so viel umständlicher.	+	Hinweis: Wir hätten auch gleich alle Klammern miteinander multiplizieren können, aber die Rechnungen wären so viel umständlicher gewesen.

Markus.bez um 08:08, 9. Jun. 2009

2009-06-09T08:08:32Z

← Nächstältere Version		Version vom 08:08, 9. Jun. 2009
Zeile 1:		Zeile 1:
-	Wir multiplizieren zuerst di ersten zwei Klammern miteinander, mit ~~hilfer ber~~ binomischen Formel	+	Wir multiplizieren zuerst die ersten zwei Klammern miteinander, mit hilfe der binomischen Formel

	{{Abgesetzte Formel\|\|<math>\begin{align}		{{Abgesetzte Formel\|\|<math>\begin{align}
Zeile 10:		Zeile 10:
	{{Abgesetzte Formel\|\|<math>(9x^4-4)(9x^4+4)=(9x^4)^2-4^2=81x^8-16\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>(9x^4-4)(9x^4+4)=(9x^4)^2-4^2=81x^8-16\,\textrm{.}</math>}}

-	Hinweis: Wir hätten auch gleich alle Klammern miteinander multiplizieren können, aber die Rechnungen währen so viel ~~unständiger~~.	+	Hinweis: Wir hätten auch gleich alle Klammern miteinander multiplizieren können, aber die Rechnungen währen so viel umständlicher.

Martin um 14:05, 28. Feb. 2009

2009-02-28T14:05:13Z

← Nächstältere Version		Version vom 14:05, 28. Feb. 2009
Zeile 1:		Zeile 1:
-	The three brackets can be multiplied together in any order, but just in this case it seems appropriate to start by multiplying the first two brackets because we can carry out the multiplication directly by using the conjugate rule,	+	Wir multiplizieren zuerst di ersten zwei Klammern miteinander, mit hilfer ber binomischen Formel

	{{Abgesetzte Formel\|\|<math>\begin{align}		{{Abgesetzte Formel\|\|<math>\begin{align}
Zeile 6:		Zeile 6:
	\end{align}</math>}}		\end{align}</math>}}

-	~~We happend to obtain an expression which can also be multiplied using the conjugate rule,~~	+	Wir verwenden hier wieder die binomische Formel für die zwei restlichen Klammern

	{{Abgesetzte Formel\|\|<math>(9x^4-4)(9x^4+4)=(9x^4)^2-4^2=81x^8-16\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>(9x^4-4)(9x^4+4)=(9x^4)^2-4^2=81x^8-16\,\textrm{.}</math>}}

-	~~Note~~: ~~If we had instead multiplied together the terms in the first and third brackets first~~, ~~we would also have got the right answer, but the calculations would have been lengthier~~.	+	Hinweis: Wir hätten auch gleich alle Klammern miteinander multiplizieren können, aber die Rechnungen währen so viel unständiger.

Tekbot: hat „Solution 2.1:2d“ nach „Lösung 2.1:2d“ verschoben: Robot: moved page

2008-10-22T13:44:25Z

hat „Solution 2.1:2d“ nach „Lösung 2.1:2d“ verschoben: Robot: moved page

← Nächstältere Version

Version vom 13:44, 22. Okt. 2008

Tekbot: Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel)

2008-10-22T08:22:08Z

Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel)

← Nächstältere Version		Version vom 08:22, 22. Okt. 2008
Zeile 1:		Zeile 1:
	The three brackets can be multiplied together in any order, but just in this case it seems appropriate to start by multiplying the first two brackets because we can carry out the multiplication directly by using the conjugate rule,		The three brackets can be multiplied together in any order, but just in this case it seems appropriate to start by multiplying the first two brackets because we can carry out the multiplication directly by using the conjugate rule,

-	{{~~Displayed math~~\|\|<math>\begin{align}	+	{{Abgesetzte Formel\|\|<math>\begin{align}
	(3x^2+2)(3x^2-2)(9x^4+4) &= \big( (3x^2)^2-2^2 \big) (9x^4+4)\\		(3x^2+2)(3x^2-2)(9x^4+4) &= \big( (3x^2)^2-2^2 \big) (9x^4+4)\\
	&= (9x^4-4)(9x^4+4)\,\textrm{.}		&= (9x^4-4)(9x^4+4)\,\textrm{.}
Zeile 8:		Zeile 8:
	We happend to obtain an expression which can also be multiplied using the conjugate rule,		We happend to obtain an expression which can also be multiplied using the conjugate rule,

-	{{~~Displayed math~~\|\|<math>(9x^4-4)(9x^4+4)=(9x^4)^2-4^2=81x^8-16\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>(9x^4-4)(9x^4+4)=(9x^4)^2-4^2=81x^8-16\,\textrm{.}</math>}}

	Note: If we had instead multiplied together the terms in the first and third brackets first, we would also have got the right answer, but the calculations would have been lengthier.		Note: If we had instead multiplied together the terms in the first and third brackets first, we would also have got the right answer, but the calculations would have been lengthier.

Tek um 08:22, 23. Sep. 2008

2008-09-23T08:22:25Z

← Nächstältere Version		Version vom 08:22, 23. Sep. 2008
Zeile 1:		Zeile 1:
-	~~{{NAVCONTENT_START}}~~	+	The three brackets can be multiplied together in any order, but just in this case it seems appropriate to start by multiplying the first two brackets because we can carry out the multiplication directly by using the conjugate rule,
-	~~<!--center> [[Image:2_1_2d.gif]] </center-->~~	+
-	The three brackets can be multiplied together in any order, but just in this case it seems appropriate to start by multiplying the first two brackets because we can carry out the multiplication directly by using the conjugate rule.	+

-	<math>	+	{{Displayed math\|\|<math>\begin{align}
-	~~\qquad~~	+
-	\begin{align}	+
	(3x^2+2)(3x^2-2)(9x^4+4) &= \big( (3x^2)^2-2^2 \big) (9x^4+4)\\		(3x^2+2)(3x^2-2)(9x^4+4) &= \big( (3x^2)^2-2^2 \big) (9x^4+4)\\
-	&= (9x^4-4)(9x^4+4)	+	&= (9x^4-4)(9x^4+4)\,\textrm{.}
-	\end{align}	+	\end{align}</math>}}
-	</math>	+

-	We happend to obtain an expression which can also be multiplied using the conjugate rule.	+	We happend to obtain an expression which can also be multiplied using the conjugate rule,

-	<math>	+	{{Displayed math\|\|<math>(9x^4-4)(9x^4+4)=(9x^4)^2-4^2=81x^8-16\,\textrm{.}</math>}}
-	~~\qquad~~	+
-	~~\begin{align}~~	+
-	(9x^4-4)(9x^4+4)=(9x^4)^2-4^2=81x^8-16	+
-	\~~end~~{~~align~~}	+
-	</math>	+

-	~~NOTE~~: If we had instead multiplied together the terms in the first and third brackets first, we would also have got the right answer, but the calculations would have been lengthier.	+	Note: If we had instead multiplied together the terms in the first and third brackets first, we would also have got the right answer, but the calculations would have been lengthier.
-		+
-	~~{{NAVCONTENT_STOP}}~~	+

Tekbot: Lösning 2.1:2d moved to Solution 2.1:2d: Robot: moved page

2008-09-09T08:34:03Z

Lösning 2.1:2d moved to Solution 2.1:2d: Robot: moved page

← Nächstältere Version

Version vom 08:34, 9. Sep. 2008

Tekbot: Robot: Automated text replacement (-[[Bild: +[[Image:)

2008-08-21T06:34:09Z

Robot: Automated text replacement (-[[Bild: +[[Image:)

← Nächstältere Version		Version vom 06:34, 21. Aug. 2008
Zeile 1:		Zeile 1:
	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
-	<!--center> [[~~Bild~~:2_1_2d.gif]] </center-->	+	<!--center> [[Image:2_1_2d.gif]] </center-->
	The three brackets can be multiplied together in any order, but just in this case it seems appropriate to start by multiplying the first two brackets because we can carry out the multiplication directly by using the conjugate rule.		The three brackets can be multiplied together in any order, but just in this case it seems appropriate to start by multiplying the first two brackets because we can carry out the multiplication directly by using the conjugate rule.

Madde um 12:53, 13. Aug. 2008

2008-08-13T12:53:29Z

← Nächstältere Version		Version vom 12:53, 13. Aug. 2008
Zeile 1:		Zeile 1:
	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
-	<center> [[Bild:2_1_2d.gif]] </center>	+	<!--center> [[Bild:2_1_2d.gif]] </center-->
	The three brackets can be multiplied together in any order, but just in this case it seems appropriate to start by multiplying the first two brackets because we can carry out the multiplication directly by using the conjugate rule.		The three brackets can be multiplied together in any order, but just in this case it seems appropriate to start by multiplying the first two brackets because we can carry out the multiplication directly by using the conjugate rule.

Madde um 12:53, 13. Aug. 2008

2008-08-13T12:53:14Z

← Nächstältere Version		Version vom 12:53, 13. Aug. 2008
Zeile 1:		Zeile 1:
	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
	<center> [[Bild:2_1_2d.gif]] </center>		<center> [[Bild:2_1_2d.gif]] </center>
		+	The three brackets can be multiplied together in any order, but just in this case it seems appropriate to start by multiplying the first two brackets because we can carry out the multiplication directly by using the conjugate rule.
		+
		+	<math>
		+	\qquad
		+	\begin{align}
		+	(3x^2+2)(3x^2-2)(9x^4+4) &= \big( (3x^2)^2-2^2 \big) (9x^4+4)\\
		+	&= (9x^4-4)(9x^4+4)
		+	\end{align}
		+	</math>
		+
		+	We happend to obtain an expression which can also be multiplied using the conjugate rule.
		+
		+	<math>
		+	\qquad
		+	\begin{align}
		+	(9x^4-4)(9x^4+4)=(9x^4)^2-4^2=81x^8-16
		+	\end{align}
		+	</math>
		+
		+	NOTE: If we had instead multiplied together the terms in the first and third brackets first, we would also have got the right answer, but the calculations would have been lengthier.
		+
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}