Solution 2.1:1h
From Förberedande kurs i matematik 1
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| - | <center> [[Bild:2_1_1h.gif]] </center> | + | We expand the quadratic with the squaring rule <math> (a+b)^2=a^2+2ab+b^2 </math>, where <math> a=5x^3 </math> and <math> b=3x^5 </math> |
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| + | <math> \qquad | ||
| + | \begin{align} | ||
| + | (5x^3 + 3x^5)^2 &= (5x^3)^2 +2\cdot 5x^3\cdot 3x^5 +(3x^5)^{2} \\ | ||
| + | &= 5^2x^{3\cdot 2} + 2\cdot 5\cdot 3\cdot x^{3+5}+ 3^2 x^{5\cdot 2}\\ | ||
| + | &= 25x^6 +30 x^8 +9x^{10}\\ | ||
| + | &= 9x^{10} +30x^8 +25x^6 | ||
| + | \end{align} | ||
| + | </math> | ||
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| + | NOTE: In the last line, we have moved the terms around so that the highest order term, <math> 9x^{10} </math>, comes first, followed by terms of decreasing order. | ||
| + | <!-- <center> [[Bild:2_1_1h.gif]] </center>--> | ||
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Revision as of 09:50, 13 August 2008
We expand the quadratic with the squaring rule \displaystyle (a+b)^2=a^2+2ab+b^2 , where \displaystyle a=5x^3 and \displaystyle b=3x^5
\displaystyle \qquad
\begin{align}
(5x^3 + 3x^5)^2 &= (5x^3)^2 +2\cdot 5x^3\cdot 3x^5 +(3x^5)^{2} \\
&= 5^2x^{3\cdot 2} + 2\cdot 5\cdot 3\cdot x^{3+5}+ 3^2 x^{5\cdot 2}\\
&= 25x^6 +30 x^8 +9x^{10}\\
&= 9x^{10} +30x^8 +25x^6
\end{align}
NOTE: In the last line, we have moved the terms around so that the highest order term, \displaystyle 9x^{10} , comes first, followed by terms of decreasing order.
