Solution 2.1:2e
From Förberedande kurs i matematik 1
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- | {{ | + | We expand the two quadratics using the squaring rule, and then sum the result |
- | + | ||
- | + | {{Displayed math||<math>\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\,\textrm{.} | ||
+ | \end{align}</math>}} |
Current revision
We expand the two quadratics using the squaring rule, and then sum the result
\displaystyle \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\,\textrm{.} \end{align} |