Solution 2.1:2e
From Förberedande kurs i matematik 1
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| - | <center> [[Bild:2_1_2e.gif]] </center> | + | We expand the two quadratics using the squaring rule, and then sum the result. |
| + | |||
| + | <math> \qquad \begin{align}(a+b)^2+(a-b)^2 &= (a^2+2ab+b^2)+(a^2-2ab+b^2)\\ | ||
| + | &= a^2+2ab+b^2+a^2-2ab+b^2 \\ | ||
| + | &= a^2+a^2+2ab-2ab+b^2+b^2\\ | ||
| + | &= 2a^2 +2b^2 | ||
| + | \end{align} | ||
| + | </math> | ||
| + | <!--<center> [[Bild:2_1_2e.gif]] </center>--> | ||
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Revision as of 13:04, 13 August 2008
We expand the two quadratics using the squaring rule, and then sum the result.
\displaystyle \qquad \begin{align}(a+b)^2+(a-b)^2 &= (a^2+2ab+b^2)+(a^2-2ab+b^2)\\ &= a^2+2ab+b^2+a^2-2ab+b^2 \\ &= a^2+a^2+2ab-2ab+b^2+b^2\\ &= 2a^2 +2b^2 \end{align}
