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Solution 2.1:2e

From Förberedande kurs i matematik 1

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Current revision (08:24, 23 September 2008) (edit) (undo)
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We expand the two quadratics using the squaring rule, and then sum the result
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We expand the two quadratics using the squaring rule, and then sum the result.
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<math> \qquad \begin{align}(a+b)^2+(a-b)^2 &= (a^2+2ab+b^2)+(a^2-2ab+b^2)\\
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{{Displayed math||<math>\begin{align}
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(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+2ab+b^2+a^2-2ab+b^2 \\
&= a^2+a^2+2ab-2ab+b^2+b^2\\
&= a^2+a^2+2ab-2ab+b^2+b^2\\
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&= 2a^2 +2b^2
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&= 2a^2 +2b^2\,\textrm{.}
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\end{align}
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\end{align}</math>}}
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</math>
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<!--<center> [[Bild:2_1_2e.gif]] </center>-->
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Current revision

We expand the two quadratics using the squaring rule, and then sum the result

(a+b)2+(a−b)2=(a2+2ab+b2)+(a2−2ab+b2)=a2+2ab+b2+a2−2ab+b2=a2+a2+2ab−2ab+b2+b2=2a2+2b2.
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