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Factorisation by Common Factors

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Question

Factorise using suitable identity: ${4 x}^{2} y^{2} - 4 x y z + z^{2}$

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Solution

$4 x^{2} y^{2} - 4 x y z + z^{2}$
$= {(2 x y)}^{2} - 2 \times 2 x y z + z^{2}$ is of the form $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$
$= {(2 x y - z)}^{2}$

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