From Förberedande kurs i matematik 1

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-	{{NAVCONTENT_START}}	+	If we consider the rule
-	<center> [[Image:2_3_1a.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>(x-a)^{2} = x^{2}-2ax+a^{2}</math>}}
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		+	and move <math>a^{2}</math> over to the left-hand side, we obtain the formula
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		+	{{Displayed math||<math>(x-a)^{2}-a^{2} = x^{2}-2ax\,\textrm{.}</math>}}
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		+	With the help of this formula, we can rewrite (complete the square of) a mixed expression <math>x^{2}-2ax</math> to a obtain a quadratic expression, <math>(x-a)^{2}-a^{2}</math>.
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		+	The expression <math>x^{2}-2x</math> corresponds to <math>a=1</math> in the formula above and thus
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		+	{{Displayed math||<math>x^{2}-2x = (x-1)^{2}-1\,\textrm{.}</math>}}

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Current revision

If we consider the rule

\displaystyle (x-a)^{2} = x^{2}-2ax+a^{2}

and move \displaystyle a^{2} over to the left-hand side, we obtain the formula

\displaystyle (x-a)^{2}-a^{2} = x^{2}-2ax\,\textrm{.}

With the help of this formula, we can rewrite (complete the square of) a mixed expression \displaystyle x^{2}-2ax to a obtain a quadratic expression, \displaystyle (x-a)^{2}-a^{2}.

The expression \displaystyle x^{2}-2x corresponds to \displaystyle a=1 in the formula above and thus

\displaystyle x^{2}-2x = (x-1)^{2}-1\,\textrm{.}