Solution 2.1:1g
From Förberedande kurs i matematik 1
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| + | The expression in the exercise is of the form <math> (a-b)^2 </math>, where <math> a=y^2</math> and <math> b=3x^2 </math>. With the help of the aquaring rule <math> (a-b)^2 =a^2 -2ab +b^2 </math>, we have | ||
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| + | <math> \begin{align} \qquad | ||
| + | (y^2-3x^3)^2 &= (y^2)^2 -2y^2\cdot 3x^3 +(3x^3)^2 \\ | ||
| + | &= y^{2\cdot 2} -6x^3y^2 +3^2x^{3\cdot 2}\\ | ||
| + | &= y^4 -6x^3y^2 +9x^6\\ | ||
| + | &= 9x^6 -6x^3y^2 +y^4 | ||
| + | \end{align} | ||
| + | </math> | ||
| + | <!-- <center> [[Bild:2_1_1g.gif]] </center> --> | ||
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Revision as of 09:32, 13 August 2008
The expression in the exercise is of the form \displaystyle (a-b)^2 , where \displaystyle a=y^2 and \displaystyle b=3x^2 . With the help of the aquaring rule \displaystyle (a-b)^2 =a^2 -2ab +b^2 , we have
\displaystyle \begin{align} \qquad (y^2-3x^3)^2 &= (y^2)^2 -2y^2\cdot 3x^3 +(3x^3)^2 \\ &= y^{2\cdot 2} -6x^3y^2 +3^2x^{3\cdot 2}\\ &= y^4 -6x^3y^2 +9x^6\\ &= 9x^6 -6x^3y^2 +y^4 \end{align}
