Lösung 2.1:4c

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If we start with the term in ''x'', we see that there is only one combination of a term from each bracket which, when multiplied, gives ''x''¹,
If we start with the term in ''x'', we see that there is only one combination of a term from each bracket which, when multiplied, gives ''x''¹,
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{{Displayed math||<math>(\underline{x}-x^{3}+x^{5})(\underline{1}+3x+5x^{2})(\underline{2}-7x^{2}-x^{4}) = \cdots + \underline{x\cdot 1\cdot 2} + \cdots</math>}}
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{{Abgesetzte Formel||<math>(\underline{x}-x^{3}+x^{5})(\underline{1}+3x+5x^{2})(\underline{2}-7x^{2}-x^{4}) = \cdots + \underline{x\cdot 1\cdot 2} + \cdots</math>}}
so, the coefficient in front of ''x'' is <math>1\cdot 2 = 2\,</math>.
so, the coefficient in front of ''x'' is <math>1\cdot 2 = 2\,</math>.
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As for ''x''², we also have only one possible combination
As for ''x''², we also have only one possible combination
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{{Displayed math||<math>(\underline{x}-x^{3}+x^{5})(1+\underline{3x}+5x^{2})(\underline{2}-7x^{2}-x^{4}) = \cdots + \underline{x\cdot 3x\cdot 2} + \cdots</math>}}
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{{Abgesetzte Formel||<math>(\underline{x}-x^{3}+x^{5})(1+\underline{3x}+5x^{2})(\underline{2}-7x^{2}-x^{4}) = \cdots + \underline{x\cdot 3x\cdot 2} + \cdots</math>}}
The coefficient in front of ''x''² is <math>3\cdot 2 = 6\,</math>.
The coefficient in front of ''x''² is <math>3\cdot 2 = 6\,</math>.

Version vom 08:23, 22. Okt. 2008

Instead of multiplying together the whole expression, and then reading off the coefficients, we investigate which terms from the three brackets together give terms in x¹ and x².

If we start with the term in x, we see that there is only one combination of a term from each bracket which, when multiplied, gives x¹,

\displaystyle (\underline{x}-x^{3}+x^{5})(\underline{1}+3x+5x^{2})(\underline{2}-7x^{2}-x^{4}) = \cdots + \underline{x\cdot 1\cdot 2} + \cdots

so, the coefficient in front of x is \displaystyle 1\cdot 2 = 2\,.

As for x², we also have only one possible combination

\displaystyle (\underline{x}-x^{3}+x^{5})(1+\underline{3x}+5x^{2})(\underline{2}-7x^{2}-x^{4}) = \cdots + \underline{x\cdot 3x\cdot 2} + \cdots

The coefficient in front of x² is \displaystyle 3\cdot 2 = 6\,.

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_2.1:4c“