Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
No jsMath TeX fonts found -- using image fonts instead.
These may be slow and might not print well.
Use the jsMath control panel to get additional information.
jsMath Control PanelHide this Message

jsMath

Solution 2.1:2d

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
(Ny sida: {{NAVCONTENT_START}} <center> Bild:2_1_2d.gif </center> {{NAVCONTENT_STOP}})
Line 1: Line 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}}

Revision as of 12:53, 13 August 2008

Bild:2_1_2d.gif

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.

(3x2+2)(3x2−2)(9x4+4)=(3x2)2−22(9x4+4)=(9x4−4)(9x4+4) 

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

(9x4−4)(9x4+4)=(9x4)2−42=81x8−16

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.

Retrieved from "http://wiki.math.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/Solution_2.1:2d"