Solution 2.1:4c
From Förberedande kurs i matematik 1
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- | {{ | + | 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 ''x''¹ and ''x''². |
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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, |
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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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+ | 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 | ||
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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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+ | The coefficient in front of ''x''² is <math>3\cdot 2 = 6\,</math>. |
Current revision
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\,.