Question
Factorise: $\text{x}^2-2\text{x}+\frac{7}{16}$
✓
Answer
$\text{x}^2-2\text{x}+\frac{7}{16}$
$=\frac{1}{16}\big(16\text{x}^2-32\text{x}+7\big)$
$=\frac{1}{16}\big(16\text{x}^2-4\text{x}-28\text{x}+7\big)$
$=\frac{1}{16}\Big[4\text{x}(4\text{x}-1)-7(4\text{x}-1)\Big]$
$=\frac{1}{16}(4\text{x}-1)(4\text{x}-7)$
$=(4\text{x}-1)\Big(\frac{\text{x}}{4}-\frac{7}{16}\Big)$
$=\frac{1}{16}\big(16\text{x}^2-32\text{x}+7\big)$
$=\frac{1}{16}\big(16\text{x}^2-4\text{x}-28\text{x}+7\big)$
$=\frac{1}{16}\Big[4\text{x}(4\text{x}-1)-7(4\text{x}-1)\Big]$
$=\frac{1}{16}(4\text{x}-1)(4\text{x}-7)$
$=(4\text{x}-1)\Big(\frac{\text{x}}{4}-\frac{7}{16}\Big)$
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