Question
Factorise the following, using the identity $a^2-2 a b+b^2=(a-b)^2$.
$\frac{\text{x}^2}{4}-2\text{x}+4$
$\frac{\text{x}^2}{4}-2\text{x}+4$
✓
Answer
$\frac{\text{x}^2}{4}-2\text{x}+4$$=\Big(\frac{\text{x}}{4}\Big)^2-2\times\frac{\text{x}}{2}\times2+2^2$
$=\Big(\frac{\text{x}}{2}-2^2\Big)$
$=\Big(\frac{\text{x}}{2}-2\Big)\Big(\frac{\text{x}}{2}-2\Big)$
$=\Big(\frac{\text{x}}{2}-2^2\Big)$
$=\Big(\frac{\text{x}}{2}-2\Big)\Big(\frac{\text{x}}{2}-2\Big)$
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