Factorise the given polynomial using suitable identity:
$4 y^{2} - 4 y + 1$

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Solution

Factorisation by using algebraic identities:
Consider the given polynomial $4 y^{2} - 4 y + 1$ ,
$4 y^{2} - 4 y + 1 = {(2 y)}^{2} - 2 (2 y) (1) + 1^{2}$
$= {(2 y - 1)}^{2} [∵ {(a - b)}^{2} = a^{2} - 2 a b + b^{2}]$
Hence, $4 y^{2} - 4 y + 1 = {(2 y - 1)}^{2}$

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