Factorise the following: $1 - 8 x + 16 x^{2}$

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Solution

Given expression is $1 - 8 x + 16 x^{2}$
We can write it as:
$= 16 x^{2} - 8 x + 1$
$= (4 x)^{2} - 2 \times 4 x + 1^{2}$
$= (4 x - 1)^{2}$ [Since $a^{2} - 2 a b + b^{2} = (a - b)^{2}$ ]

Hence, $1 - 8 x + 16 x^{2} = (4 x - 1)^{2}$ .

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